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? a. 3 cm b. 5 cm c. 8 cm d. 12 cm

Explanation:

Step1: Solve the quadratic equation

Given the equation \(x^{2}+5x = 24\), rewrite it in standard form \(x^{2}+5x - 24=0\).
Factor the quadratic: \((x + 8)(x - 3)=0\).
Set each factor equal to zero: \(x+8 = 0\) gives \(x=-8\), \(x - 3=0\) gives \(x = 3\).
Since length cannot be negative, we consider \(x = 3\).

Answer:

A. \(3\mathrm{cm}\)