Question

The area of a rectangle is 24 square centimeters. The length (X), in centimeters of the rectangle is given by the equation x2 + 5x = 24.
What is the length of the rectangle?

Answer 1

The length of the rectangle is 3 cm

Applications of Quadratic equations

From the question, we are to determine the value of the length of the rectangle

To find the length of the rectangle, we will determine the value of x in the given equation

The given equation is

$x^{2} + 5x =24$

This can be written as

$x^{2} +5x -24 =0$

Factorizing

$x^{2} +8x - 3x -24 = 0$

$x(x+8) -3(x+8)=0$

$(x-3)(x+8)=0$

Then,

$x-3 = 0$ OR $x + 8 = 0$

x = 3 OR x = -8

Since, the length of the rectangle cannot be negative, the value of x is 3.

Hence, the length of the rectangle is 3 cm.

Learn more on solving quadratic equations here: brainly.com/question/8649555