Question

The rectangle has an area of 24 square centimeters. Find the length a of the rectangle.

The Length of the rectangle is A and the Width of the rectangle is A - 5

Answer 1

To find the length of the rectangle with an area of 24 square centimeters and width of (a-5), solve the quadratic equation a^2 - 5a - 24 = 0, which gives a length a = 8 centimeters.

Step-by-step explanation:

The question asks us to find the length a of a rectangle that has an area of 24 square centimeters, given that the width is a-5. Since area of a rectangle is found by multiplying the length by the width, we can set up the equation a*(a-5) = 24. To find the value of a, we need to solve this quadratic equation.

First, we expand the equation:

a² - 5a = 24

Then, we set the equation to zero:

a² - 5a - 24 = 0

Next, we factor the quadratic equation:

(a - 8)(a + 3) = 0

There are two possible solutions for a:

• a = 8
• a = -3

Since a length cannot be negative, we discard a = -3 and conclude that the length a of the rectangle is 8 centimeters.