A suitcase measures 24 inches long and the dialogue is 30 inches long. How much material is needed to cover one side of the suitcase?

432 in.^2

Step-by-step explanation:

The side of the suitcase is a rectangle. One length is 24 inches. The diagonal of the rectangle is 30 inches long. The diagonal is a hypotenuse of a right triangle. The length is a leg. We need to find the other leg.

We use the Pythagorean theorem,

a^2 + b^2 = c^2

(24 in.) ^2 + b^2 = (30 in.) ^2

576 in.^2 + b^2 = 900 in.^2

b^2 = 324 in.^2

b = sqrt (324 in^2)

b = 18 in

area of rectangle = length * width

A = 24 in. * 18 in.

A = 432 in.^2