Word Problems

Question

Find the lengths of the sides of the rectangle if it is known that one of them is 14 cm bigger than the other, and the diagonal of the rectangle is 34 cm.

Find the lengths of the sides of the rectangle if it is known that one of them is 14 cm bigger than the other, and the diagonal of the rectangle is 34 cm.

Answer 1

So, let "x" be one side of the rectangle. You know the other side is "14 + x."

 

The diagonal is helpful because we can apply Pythagorean's theorem such that:

 

34² = x² + (14 + x)². Let's expand the right side, knowing the left side is 1,156.

 

So, x² + 196 + 28x + x² = 2x² + 28x + 196 = 1156.

 

Subtract 196 from both sides, and you get 2x² + 28x = 960

 

We can divide through by 2 and solve for the quadratic equation either via the quadratic formula or factorization.

 

x² + 14x - 480 = 0  => (x - 16)(x + 30)= 0

 

x can't be a negative # so x = 16. Plug it into the formulas to double-check if you're curious.