Lateral area of a right rectangular prism is 144 cm². Its length is three times its width and its height is twice its width. Find surface area in centimeters squared

Step-by-step explanation:

Given that, the lateral area is 144cm².

Length is 3 * width

Height is 2 * width

Let width be x

Then length is 3x

Height = 2x

Given that lateral area is 144cm²

The formula for lateral area of a rectangular prism is

A_L = Base perimeter. * height

A_L = Ph = (2L + 2W) •h

144 = (2 * 3x + 2 * x) * 2x

144 = (6x + 2x) * 2x

144 = 8x * 2x

144 = 16x²

x² = 144 / 16

x = √ (144 / 16)

x = √9

x = 3

So, the width is 3cm

Height is 6cm

Lenght is 9cm

So the total surface area of a rectangular prism becomes

A = 2 (LW + LH + WH)

A = 2 (9*3 + 9 * 6 + 3 * 6)

A = 2 (27 + 54 + 18)

A = 2 * 99

A = 198 cm²