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 = 6 cm; width = 7 cm
C)length = 4 cm; width = 9 cm
D)length = 7 cm; width = 6 cm

Answer 1

Let w and l be the length and height of the rectangle.

We know that:

`\begin{cases}l = 2w-5\\2(l+w)=26\end{cases}`

Substitute the first equation in the second:

`2(l+w)=26 \iff l+w=13 \iff 2w-5+w=13 \iff 3w = 18 \iff w=6`

Use the first equation to compute the length:

`l=2* 6 - 5 = 12-5=7`

So, length = 7 cm; width = 6 cm