Question

which is the area of the rectangle?

a. 7,935 square units
b. 11,500 square units
c. 13,248 square units
d. 14,835 square units

Explanation:

Step1: Find the length of the other side of the rectangle

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Here, \(a = 69\), \(c=115\), and we want to find \(b\).

$$b=\sqrt{c^{2}-a^{2}}=\sqrt{115^{2}-69^{2}}=\sqrt{(115 + 69)(115 - 69)}=\sqrt{184\times46}=\sqrt{8464}=92$$

Step2: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A=\text{length}\times\text{width}\). The length is \(100 + 92=192\) and the width is \(69\)

$$A=192\times69=(200 - 8)\times69=200\times69-8\times69=13800-552 = 13248$$

Answer:

C. 13,248 square units