Question

One side of a rectangle is 6 centimeters shorter than six times another side. Find the length of the shorter side if we also know that the perimeter of the rectangle is 156 centimeters.

Answer 1

length of the shorter side is 12cm

Explanation:

let one of the side of th rectangle = x

six times this side = 6x

Another side is 6cm shorter than six times the previous side

this side = 6x - 6

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

let the unknown side = width = x

let the length = 6x - 6

The perimeter of the triangle is given as 156 cm

Perimeter = 2(6x - 6 + x)

156 = 2(6x - 6 + x)

solve for x:

156 = 2(7x - 6)

divide both sides by 2:

$\begin{gathered} \frac{156}{2}=2(\frac{7x -6}{2}) \\ 78\text{ = 7x - 6} \end{gathered}$$\begin{gathered} \text{Add 6 to both sides:} \\ 78\text{+ 6 = 7x } \\ 84\text{ = 7x} \end{gathered}$$\begin{gathered} \text{divide both sides by 7:} \\ \frac{84}{7}\text{ = }\frac{7x}{7} \\ x\text{ = 12} \end{gathered}$

The width = x = 12

The length = 6x - 6 = 6(12) - 6

The length = 66

From the above, we see the length of the shorter side is 12cm