Question: The length of a rectangle is 7 in more than its width. The perimeter of the rectangle is 110 in. Find its length and width.


A ) 62, 55
B ) 26, 115
C ) 29, 26
D ) 31, 24

Steps to derive

1 Let l represent the length of the rectangle.

2 Let w represent the width of the rectangle.

3 l - w = 7 ---------- (1)

4 The perimeter of a rectangle = 2 (length + width).

5 2(l + w) = 110

6 l + w = 55 --------------- (2)
 [Divide throughout by 2.]

7 Solve the system of linear equations by using the addition method:

8 l - w = 7
l + w = 55
-----------
2l      = 62    [Add.]

9 l = 31
 [Solve for l.]

10 31 - w = 7
 [Substitute the value of l in equation (1).]

11 w = 24

12 So, the length of the rectangle is 31 in and its width is 24 in



Hence the right answer is Option D

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