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

To find out how much material is needed to cover one side of the suitcase, we need to find the area of the rectangle that forms one side of the suitcase.

The area of a rectangle is given by the formula: Area = length * width

We know the length of the suitcase is 24 inches. However, we don't know the width. But we do know the diagonal and the length, and we can use the Pythagorean theorem to find the width.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c²

In this case, the diagonal of the suitcase is the hypotenuse of a right triangle, and the length and width of the suitcase are the other two sides. So we can write the equation as: length² + width² = diagonal²

Substituting the given values into the equation gives us: 24² + width² = 30²

Solving for width² gives us: width² = 30² - 24² = 900 - 576 = 324

Taking the square root of both sides gives us: width = √324 = 18 inches

Now that we know the width, we can find the area of one side of the suitcase: Area = length