Question

A trapezoid has a perimeter of 14 feet. What will the perimeter be if each side length is increased by a factor 7? 21 feet 98 feet 196 feet 686 feet

Answer 1

The correct answer is:

B. 98 feet

The perimeter be 98 feet if each side length is increased by a factor 7.

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Answer 2

Correct choice is B

Explanation:

Let a, b, c and d be the trapezoid's sides lengths.

The perimeter of the trapezoid is the sum of all sides lengths, thus,

`a+b+c+d=14\ ft.`

If each side length is increased by a factor 7, then new sides have lengths 7a, 7b, 7c and 7d. The perimeter of new trapezoid is

`7a+7b+7c+7d.`

Use the distributive property for this expression:

`7a+7b+7c+7d=7(a+b+c+d).`

Since
`a+b+c+d=14\ ft,` then

`7a+7b+7c+7d=7(a+b+c+d)=7\cdot 14=98\ ft.`