Question

the area of a rectangle is 105 square inches. the length of the longest side of the rectangle is 15 inches. what is the length, in inches, of the shortest side of this rectangle?
a. 7
b. 15
c. 30
d. 90

Explanation:

Step1: Recall the formula for the area of a rectangle

The area formula of a rectangle is \(A = l\times w\), where \(A\) is the area, \(l\) is the length (longest side), and \(w\) is the width (shortest side).

Step2: Substitute the known values into the formula

We know that \(A = 105\) square inches and \(l=15\) inches. Substituting into \(A = l\times w\), we get \(105=15\times w\).

Step3: Solve for \(w\)

To find \(w\), we use the equation \(w=\frac{A}{l}\). So \(w = \frac{105}{15}\).
Since \(15\times7 = 105\), then \(w = 7\) inches.

Answer:

A. 7