One side of a rectangle is 4 inches longer than the other side. the area of the rectangle is 21 square inches. find the lengths of each side.

l = 7 in; w = 3 in

Step-by-step explanation:

The formula for the area of a rectangle is

A = lw

Data:

A = 21 in²

l = w + 4

Calculation:

                 21 = (w + 4) × w

                 21 = w² + 4w

w² + 4w - 21 = 0

(w + 7)(w - 3) = 0

w + 7 = 0     w - 3 = 0

      w = -7         w = 3

We reject the negative value, so w = 3 in.

21 = l × 3

l = 7

The rectangle is 7 in long and 3 in wide.

Additional information required is ∠L ≅ ∠P

Step-by-step explanation:

The ASA congruence theorem is the Angle-Side-Angle Theorem where 2 angles and the side included between these 2 angles should be congruent.

Given that KL ≅ QP and ∠K ≅ ∠Q.

Now that one congruent angle and one side are found, the other angle is  additionally needed.

⇒ Additional information required is ∠L ≅ ∠P