Question

The perimeter of the rectangle below is 64 units. Find the length of side PS. Write your answer without variables.

Answer 1

Given:

The perimeter of the rectangle, P=64 units.

From the figure, the length of the rectangle, l=PQ=3x+3.

The breadth of the rectangle, b=PS=2x-1.

Now, the expression for the perimeter of the rectangle can be written as,

`\begin{gathered} P=2(l+b) \\ P=2(3x+3+2x-1) \\ P=2(5x+2) \\ P=2*5x+2*2 \\ P=10x+4 \end{gathered}`

Now, put P=64 in the above equation and solve for x.

`\begin{gathered} 64=10x+4 \\ 64-4=10x \\ 60=10x \\ (60)/(10)=x \\ 6=x \end{gathered}`

Now, we know b=PS=2x-1.

Hence, PS can be calculated as,

`\begin{gathered} PS=2x-1 \\ =2*6-1 \\ =12-1 \\ =11 \end{gathered}`

Therefore, the length of side PS is 11 units.