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\\\\(70)/(10)=z\\\\z=7`

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

`PQ=2(7)+2=16\ units`