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Basic Geometry : How to find the perimeter of a 45/45/90 right isosceles triangle

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Example Question #21 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Find the perimeter.

Possible Answers:

46.22

45.71

44.38

48.72

Correct answer:

44.38

Explanation:

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then .

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$b=13\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\text{Perimeter}=13+13+13\sqrt2=44.38$

Make sure to round to two places after the decimal.

Report an Error

Example Question #142 : 45/45/90 Right Isosceles Triangles

Find the perimeter.

Possible Answers:

69.82

74.58

71.70

72.49

Correct answer:

71.70

Explanation:

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then .

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$b=21\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\text{Perimeter}=21+21+21\sqrt2=71.70$

Make sure to round to two places after the decimal.

Report an Error

Example Question #22 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Find the perimeter.

Possible Answers:

75.11

78.21

80.45

88.47

Correct answer:

75.11

Explanation:

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then .

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$b=22\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\text{Perimeter}=22+22+22\sqrt2=75.11$

Make sure to round to two places after the decimal.

Report an Error

Example Question #23 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Find the perimeter.

Possible Answers:

89.56

82.40

77.21

81.94

Correct answer:

81.94

Explanation:

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then .

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$b=24\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\text{Perimeter}=24+24+24\sqrt2=81.94$

Make sure to round to two places after the decimal.

Report an Error

Example Question #24 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Find the perimeter.

Possible Answers:

71.22

80.59

79.29

78.53

Correct answer:

78.53

Explanation:

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then .

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$b=23\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\text{Perimeter}=23+23+23\sqrt2=78.53$

Make sure to round to two places after the decimal.

Report an Error

Example Question #25 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Find the perimeter.

Possible Answers:

79.84

84.22

85.36

85.30

Correct answer:

85.36

Explanation:

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then .

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$b=25\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\text{Perimeter}=25+25+25\sqrt2=85.36$

Make sure to round to two places after the decimal.

Report an Error

Example Question #26 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Find the perimeter.

Possible Answers:

76.66

94.21

88.77

90.90

Correct answer:

88.77

Explanation:

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then .

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$b=26\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\text{Perimeter}=26+26+26\sqrt2=88.77$

Make sure to round to two places after the decimal.

Report an Error

Example Question #27 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Find the perimeter.

Possible Answers:

95.60

94.21

97.89

98.04

Correct answer:

95.60

Explanation:

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then .

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$b=28\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\text{Perimeter}=28+28+28\sqrt2=95.60$

Make sure to round to two places after the decimal.

Report an Error

Example Question #28 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Find the perimeter.

Possible Answers:

102.54

99.01

101.21

97.86

Correct answer:

99.01

Explanation:

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then .

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$b=29\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\text{Perimeter}=29+29+29\sqrt2=99.01$

Make sure to round to two places after the decimal.

Report an Error

Example Question #29 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Find the perimeter.

Possible Answers:

102.43

99.58

104.52

110.09

Correct answer:

102.43

Explanation:

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then .

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$b=30\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\text{Perimeter}=30+30+30\sqrt2=102.43$

Make sure to round to two places after the decimal.

Report an Error

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Basic Geometry : How to find the perimeter of a 45/45/90 right isosceles triangle

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #21 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Example Question #142 : 45/45/90 Right Isosceles Triangles

Example Question #22 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Example Question #23 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Example Question #24 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Example Question #25 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Example Question #26 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Example Question #27 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Example Question #28 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Example Question #29 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

All Basic Geometry Resources

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