Question

Here are two rectangles.

EH = 10 cm
BC= EF
The perimeter of ABCD is 25 cm.
The area of EFGH is 35 cm²
2
Find the length of AB.

Answer 1

The length of AB is 9 cm.

Explanation:

EH = 10 cm, area of EFGH is 35 cm, so

EF = 3.5 cm

BC = AD = 3.5 cm, perimeter of ABCD = 25 cm, so AB = 9 cm since 2(9 + 3.5) = 2(12.5) = 25

Answer 2

The calculated length of the segment AB in the rectangle ABCD is 9 cm

How to determine the length of the segment AB

From the question, we have the following parameters that can be used in our computation:

EH = 10 cm

BC = EF

Area of ABCD = 25

Perimeter of EFGH = 35 square cm

The area of a rectangle is the product of the side lengths

So, we have

A = EF * EH

This gives

EF * 10 = 35

EF = 3.5

The perieter of a rectangle is the sum of the side lengths

For ABCD, we have

P = 2 * (AB + BC)

Recall that

BC = EF

So, we have

2 * (AB + 3.5) = 25

Next, we have

AB + 3.5 = 12.5

Evaluate the like terms

AB = 9

Hence, the length of the segment AB is 9 cm