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Basic Geometry : 45/45/90 Right Isosceles Triangles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #1121 : Plane Geometry

Find the perimeter.

Possible Answers:

48.72

45.71

46.22

44.38

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 #1121 : Plane Geometry

Find the perimeter.

Possible Answers:

72.49

71.70

69.82

74.58

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 #1122 : Plane Geometry

Find the perimeter.

Possible Answers:

78.21

75.11

88.47

80.45

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 #144 : 45/45/90 Right Isosceles Triangles

Find the perimeter.

Possible Answers:

81.94

89.56

82.40

77.21

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 #1124 : Basic Geometry

Find the perimeter.

Possible Answers:

71.22

78.53

79.29

80.59

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 #146 : 45/45/90 Right Isosceles Triangles

Find the perimeter.

Possible Answers:

79.84

85.36

84.22

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 #1123 : Plane Geometry

Find the perimeter.

Possible Answers:

88.77

76.66

90.90

94.21

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 #1131 : Plane Geometry

Find the perimeter.

Possible Answers:

94.21

95.60

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 #1131 : Plane Geometry

Find the perimeter.

Possible Answers:

99.01

101.21

102.54

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 #141 : 45/45/90 Right Isosceles Triangles

Find the perimeter.

Possible Answers:

104.52

99.58

102.43

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 : 45/45/90 Right Isosceles Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1121 : Plane Geometry

Example Question #1121 : Plane Geometry

Example Question #1122 : Plane Geometry

Example Question #144 : 45/45/90 Right Isosceles Triangles

Example Question #1124 : Basic Geometry

Example Question #146 : 45/45/90 Right Isosceles Triangles

Example Question #1123 : Plane Geometry

Example Question #1131 : Plane Geometry

Example Question #1131 : Plane Geometry

Example Question #141 : 45/45/90 Right Isosceles Triangles

All Basic Geometry Resources

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