Question

A rectangle has a length of 4 feet and a perimeter of 14 feet. What is the perimeter of a similar rectangle with a width of 9 feet? **We are learning about proportions**
A. 36 ft
B. 108 ft
C. 42 ft
D. 126 ft​

Answer 1

Answer:

Option C. $42\ ft$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor and the ratio of its perimeter is equal to the scale factor too

step 1

Find the width of the rectangle that has a length of 4 feet and a perimeter of 14 feet

The perimeter of a rectangle is equal to

$P=2(L+W)$

substitute the values and solve for W

$14=2(4+W)$

$W=7-4=3\ ft$

step 2

Find the scale factor

Let

z-----> the scale factor

To find the scale factor divide the width of the larger rectangle by the width of the smaller rectangle

so

$9/3=3$

step 3

Find the perimeter of the larger rectangle

To find the perimeter of the larger rectangle multiply the perimeter of the smaller rectangle by the scale factor

so

$3*14=42\ ft$