Answer:
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