Question

The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 26 cm. What are the dimensions of the rectangle?

A. length = 5 cm; width = 5 cm
B. length = 7 cm; width = 6 cm
C. length = 6 cm; width = 7 cm
D. length = 4 cm; width = 9 cm ...?

Answer 1

Here is the solution to the given problem above.
Given:
Let x be the width and L for length.
L= 2x -5
P = 2w + 2L
26 = 2x + 2(2x -5)
26 = 2x +4x - 10
26 = 6x -10
26 +10 =6x
36 =6x <<< divide both sides by 6
and we get x =6
Therefore the width is 6 centimeters.
Now to find the length.
L = 2x - 5 <<< substitute x with 6.
L = 2(6) - 5
L = 7
Length is 7 centimeters.
Therefore, the final answer would be option B. Length = 7 cm and width is 6cm.
Hope this answer helps.

Answer 2

l = 2w - 5 . . . (1)
2l + 2w = 26
l + w = 13 . . . (2)

Putting (1) into (2), gives
2w - 5 + w = 13
3w = 13 + 5 = 18
w = 18/3 = 6
l = 2(6) - 5 = 12 - 5 = 7

Therefore, length = 7 cm and width = 6 cm. (option B)