Question

The perimeter of the rectangle blow is 70 units find the length of side PS

Answer 1

The perimeter of the given rectangle is 78 units.

Recall that the perimeter of a rectangle is given by

`P=2(w+l)`

Where w is the width and l is the length of the rectangle.

As you can see from the given figure,

w = 3z + 3

l = 4z + 1

We are asked to find the side length of side PS.

Substitute the given values into the above formula and solve for z.

`\begin{gathered} P=2(w+l) \\ 78=2(3z+3+4z+1_{}) \\ 78=2(7z+4_{}) \\ (78)/(2)=(7z+4_{}) \\ 39=7z+4_{} \\ 39-4=7z \\ 35=7z \\ (35)/(7)=z \\ 5=z \end{gathered}`

So, the value of z is 5

Finally, the length of side PS is

`\begin{gathered} PS=4z+1 \\ PS=4(5)+1 \\ PS=20+1 \\ PS=21 \end{gathered}`

Therefore, the length of the side PS is 21 units.