ISEE Middle Level Math : How to find the perimeter of the rectangle

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

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Example Questions

Example Question #248 : Geometry

Find the perimeter of a rectangle with a length of 36cm and a width that is a third of the length.

Possible Answers:

\(\displaystyle 48\text{cm}\)

\(\displaystyle 108\text{cm}\)

\(\displaystyle 56\text{cm}\)

\(\displaystyle 64\text{cm}\)

\(\displaystyle 96\text{cm}\)

Correct answer:

\(\displaystyle 96\text{cm}\)

Explanation:

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

\(\displaystyle P = a+b+c+d\)

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

 

Now, we know the length of the rectangle is 36cm.  Because it is a rectangle, the opposite side is also 36cm.  We also know the width is a third of the length.  Therefore, the width is 12cm.  Because it is a rectangle, the opposite side is also 12cm.

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

\(\displaystyle P = 36\text{cm} + 36\text{cm} +12\text{cm} + 12\text{cm}\)

\(\displaystyle P = 96\text{cm}\)

Example Question #249 : Geometry

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

Possible Answers:

\(\displaystyle 60\text{in}\)

\(\displaystyle 56\text{in}\)

\(\displaystyle 72\text{in}\)

\(\displaystyle 48\text{in}\)

\(\displaystyle 24\text{in}\)

Correct answer:

\(\displaystyle 60\text{in}\)

Explanation:

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

\(\displaystyle P = a+b+c+d\)

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 four times the width.  Therefore, the length is 24in.  Because it is a rectangle, the opposite side is also 24in.

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

\(\displaystyle P = 6\text{in} + 6\text{in} + 24\text{in} + 24\text{in}\)

\(\displaystyle P = 60\text{in}\)

Example Question #250 : Geometry

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

Possible Answers:

\(\displaystyle 24\text{cm}\)

\(\displaystyle 36\text{cm}\)

\(\displaystyle 12\text{cm}\)

\(\displaystyle 16\text{cm}\)

\(\displaystyle 28\text{cm}\)

Correct answer:

\(\displaystyle 28\text{cm}\)

Explanation:

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

\(\displaystyle P = a+b+c+d\)

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

\(\displaystyle P = 2\text{cm} + 2\text{cm} + 12\text{cm} + 12\text{cm}\)

\(\displaystyle P = 28\text{cm}\)

Example Question #251 : Geometry

Use the following rectangle to answer the question:

Rectangle4

Find the perimeter.

Possible Answers:

\(\displaystyle 48\text{cm}\)

\(\displaystyle 16\text{cm}\)

\(\displaystyle 32\text{cm}\)

\(\displaystyle 21\text{cm}\)

\(\displaystyle 63\text{cm}\)

Correct answer:

\(\displaystyle 32\text{cm}\)

Explanation:

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

\(\displaystyle P = a+b+c+d\)

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

\(\displaystyle P = 9\text{cm} +9\text{cm} + 7\text{cm} + 7\text{cm}\)

\(\displaystyle P = 32\text{cm}\)

Example Question #252 : Geometry

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

Possible Answers:

\(\displaystyle 36\text{in}\)

\(\displaystyle 18\text{in}\)

\(\displaystyle 48\text{in}\)

\(\displaystyle 108\text{in}\)

\(\displaystyle 9\text{in}\)

Correct answer:

\(\displaystyle 48\text{in}\)

Explanation:

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

\(\displaystyle P = a+b+c+d\)

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

\(\displaystyle P = 6\text{in} + 6\text{in} + 18\text{in} + 18\text{in}\)

\(\displaystyle P = 48\text{in}\)

Example Question #253 : Geometry

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

Possible Answers:

\(\displaystyle 14\text{cm}\)

\(\displaystyle 36\text{cm}\)

\(\displaystyle 48\text{cm}\)

\(\displaystyle 32\text{cm}\)

\(\displaystyle 24\text{cm}\)

Correct answer:

\(\displaystyle 32\text{cm}\)

Explanation:

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

\(\displaystyle P = a+b+c+d\)

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. 

\(\displaystyle P = 4\text{cm} + 4\text{cm} + 12\text{cm} + 12\text{cm}\)

\(\displaystyle P = 32\text{cm}\)

Example Question #254 : Geometry

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

Possible Answers:

\(\displaystyle 24\text{in}\)

\(\displaystyle 42\text{in}\)

\(\displaystyle 36\text{in}\)

\(\displaystyle 18\text{in}\)

\(\displaystyle 48\text{in}\)

Correct answer:

\(\displaystyle 36\text{in}\)

Explanation:

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

\(\displaystyle P = a+b+c+d\)

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

\(\displaystyle P = 6\text{in} + 6\text{in} + 12\text{in} + 12\text{in}\)

\(\displaystyle P = 36\text{in}\)

Example Question #255 : Geometry

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

Possible Answers:

\(\displaystyle 20\text{cm}\)

\(\displaystyle 48\text{cm}\)

\(\displaystyle 16\text{cm}\)

\(\displaystyle 36\text{cm}\)

\(\displaystyle 40\text{cm}\)

Correct answer:

\(\displaystyle 40\text{cm}\)

Explanation:

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

\(\displaystyle P = a+b+c+d\)

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

\(\displaystyle P = 16\text{cm} + 16\text{cm} + 4\text{cm} + 4\text{cm}\)

\(\displaystyle P = 40\text{cm}\)

Example Question #256 : Geometry

Find the perimeter of a rectangle with an area of \(\displaystyle 50\), and a base length of \(\displaystyle 2\).

Possible Answers:

\(\displaystyle 54\)

\(\displaystyle 104\)

\(\displaystyle 45\)

\(\displaystyle 52\)

\(\displaystyle 58\)

Correct answer:

\(\displaystyle 54\)

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.

\(\displaystyle A=bh\)

\(\displaystyle 50=2h\)

Divide by two on both sides to obtain the height.

\(\displaystyle \frac{50}{2}=\frac{2h}{2}\)

\(\displaystyle h=25\)

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

The formula for the perimeter is:

\(\displaystyle P=2b+2h\)

Substitute the values to find the perimeter.

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

The perimeter is:  \(\displaystyle 54\)

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