Question

The perimeter of the rectangle is 76 units. Find the length of side pq

Answer 1

Answer:   $PQ=16\ units$

Step-by-step explanation:

The missing figure is attached.

The perimeter of a rectangle is:

$P=2l+2w$

Where "l" is the lenght and "w" is the width.

You can identify in the figure that:

$w=SR=PQ=2z+2\\\\l=QR=PS=3z+1$

Then, knowing the perimeter of the rectangle, you can make the subsitution into the formula:

 $76=2(3z+1)+2(2z+2)$

Now you must simplify and solve for "z"

$76=6z+2+4z+4\\\\76-6=10z\\\\70=10z\\\\\frac{70}{10}=z\\\\z=7$

Finally, substituting the value of "z" into  $PQ=2z+2$, you get:

 $PQ=2(7)+2=16\ units$