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ISEE Middle Level Math : Rectangles

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Example Question #33 : How To Find The Perimeter Of The Rectangle

Find the perimeter of a rectangle with a width of 2cm and a length that is six times the width.

Possible Answers:

$28\text{cm}$

$36\text{cm}$

$12\text{cm}$

$24\text{cm}$

$16\text{cm}$

Correct answer:

$28\text{cm}$

Explanation:

To find the perimeter of a rectangle, we will use the following formula:

P = a+b+c+d

Where a, b, c, and d are the lengths of the sides of the rectangle.

Now, we know the width of the rectangle is 2cm. Because it is a rectangle, the opposite side is also 2cm.

We know the length is six times the width. Therefore, the length is 12cm. Because it is a rectangle, the opposite side is also 12cm.

Knowing this, we can substitute into the formula. We get

$P = 2\text{cm} + 2\text{cm} + 12\text{cm} + 12\text{cm}$

$P = 28\text{cm}$

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Example Question #251 : Plane Geometry

Use the following rectangle to answer the question:

Rectangle4

Find the perimeter.

Possible Answers:

$63\text{cm}$

$32\text{cm}$

$48\text{cm}$

$16\text{cm}$

$21\text{cm}$

Correct answer:

$32\text{cm}$

Explanation:

To find the perimeter of a rectangle, we will use the following formula:

P = a+b+c+d

Where a, b, c, and d are the lengths of the sides of the rectangle.

Now, given the rectangle,

Rectangle4

we can see the length is 9cm. Because it is a rectangle, the opposite side is also 9cm.

We can see the width is 7cm. Because it is a rectangle, the opposite side is also 7cm.

Knowing this, we can substitute into the formula. We get

$P = 9\text{cm} +9\text{cm} + 7\text{cm} + 7\text{cm}$

$P = 32\text{cm}$

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Example Question #252 : Plane Geometry

Find the perimeter of a rectangle with a width of 6in and a length that is three times the width.

Possible Answers:

$9\text{in}$

$18\text{in}$

$108\text{in}$

$48\text{in}$

$36\text{in}$

Correct answer:

$48\text{in}$

Explanation:

To find the perimeter of a rectangle, we will use the following formula:

P = a+b+c+d

Where a, b, c, and d are the lengths of the sides of the rectangle.

Now, we know the width of the rectangle is 6in. Because it is a rectangle, the opposite side is also 6in.

We know the length is three times the width. Therefore, the length is 18in. Because it is a rectangle, the opposite side is also 18in.

So, we can substitute. We get

$P = 6\text{in} + 6\text{in} + 18\text{in} + 18\text{in}$

$P = 48\text{in}$

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Example Question #253 : Plane Geometry

Find the perimeter of a rectangle with a width of 4cm and a length that is three times the width.

Possible Answers:

$32\text{cm}$

$36\text{cm}$

$24\text{cm}$

$48\text{cm}$

$14\text{cm}$

Correct answer:

$32\text{cm}$

Explanation:

To find the perimeter of a rectangle, we will use the following formula:

P = a+b+c+d

Where a, b, c, and d are the lengths of the sides of the rectangle.

Now, we know the width of the rectangle is 4cm. Because it is a rectangle, the opposite side is also 4cm.

We know the length is three times the width. Therefore, the length is 12cm. Because it is a rectangle, the opposite side is also 12cm.

So, we can substitute.

$P = 4\text{cm} + 4\text{cm} + 12\text{cm} + 12\text{cm}$

$P = 32\text{cm}$

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Example Question #254 : Plane Geometry

Find the perimeter of a rectangle with a width of 6in and a length that is two times the width.

Possible Answers:

$24\text{in}$

$18\text{in}$

$48\text{in}$

$42\text{in}$

$36\text{in}$

Correct answer:

$36\text{in}$

Explanation:

To find the perimeter of a rectangle, we will use the following formula:

P = a+b+c+d

Where a, b, c, and d are the lengths of the sides of the rectangle.

Now, we know the width of the rectangle is 6in. Because it is a rectangle, the opposite side is also 6in.

We know the length is two times the width. Therefore, the length is 12in. Because it is a rectangle, the opposite side is also 12in.

So, we get

$P = 6\text{in} + 6\text{in} + 12\text{in} + 12\text{in}$

$P = 36\text{in}$

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Example Question #251 : Geometry

Find the perimeter of a rectangle with a length of 16cm and a width that is a quarter of the length.

Possible Answers:

$40\text{cm}$

$36\text{cm}$

$16\text{cm}$

$20\text{cm}$

$48\text{cm}$

Correct answer:

$40\text{cm}$

Explanation:

To find the perimeter of a rectangle, we will use the following formula:

P = a+b+c+d

Where a, b, c, and d are the lengths of the sides of the rectangle.

Now, we know the length of the rectangle is 16cm. Because it is a rectangle, the opposite side is also 16cm. We also know the width of the rectangle is a quarter of the length. To find the width, we will divide 16 by 4. Therefore, the width is 4cm. Because it is a rectangle, the opposite side is also 4cm.

Knowing this, we can substitute into the formula. We get

$P = 16\text{cm} + 16\text{cm} + 4\text{cm} + 4\text{cm}$

$P = 40\text{cm}$

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Example Question #256 : Plane Geometry

Find the perimeter of a rectangle with an area of , and a base length of .

Possible Answers:

104

Correct answer:

Explanation:

This problem requires finding the height of the rectangle first.

Write the formula for the area of the rectangle, and substitute the known values.

A=bh

50=2h

Divide by two on both sides to obtain the height.

$\frac{50}{2}=\frac{2h}{2}$

h=25

The perimeter of a rectangle includes 2 bases and 2 heights.

The formula for the perimeter is:

P=2b+2h

Substitute the values to find the perimeter.

P=2(2)+2(25) = 4+50 = 54

The perimeter is:

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ISEE Middle Level Math : Rectangles

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #33 : How To Find The Perimeter Of The Rectangle

Example Question #251 : Plane Geometry

Example Question #252 : Plane Geometry

Example Question #253 : Plane Geometry

Example Question #254 : Plane Geometry

Example Question #251 : Geometry

Example Question #256 : Plane Geometry

All ISEE Middle Level Math Resources

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