Question

One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 18 cm². Find the lengths of all sides.

No Spam​

Answer 1

Answer:

Let x be the length of the longer side x > 3 , then the order side's length is x - 3 cm.

Then the area is S1 = x(x - 3) cm². After we increase the lengths of the sides they will become ( x+1 ) and ( x-3+1 ) = (x-2) cm long.

Hence, the area of the new rectangle will be A2 = ( x+1 ) × ( x-2 ) cm² , which is 18cm² more than the first area.

Therefore,

A1 + 18 = A2

x(x - 3) + 18 = ( x + 1 ) ( x - 2 )

x² - 3x + 18 = x² + x - 2x - 2

2x = 20

x = 10.

So, the sides of the rectangle are 10 cm and ( 10-3 ) = 7 cm long.

hope it helps you.

Answer 2