The sum of length, breadth and height of a rectangular parallelopiped is 20 cm.and its whole surface area is 264 sq. cm. Find the area of the square whose side is equal to the length of the diagonal of the parallelopiped.

(1) 136 square cm. (2) 120 square cm. (3) 125 square cm. (4) 100 square cm.

Solution:

Let the length, breadth and height of the parallelopiped be a, b and c cm respectively.

:. a+ b+ c= 20

2 (ab + bc + ca) = 264

:. (a+b+c)²= a²+b²+c²+2(ab + bc+ ca)

⇒400= a²+b²+c²+264

⇒a²+b²+c²= 400-264

=136 sq. cm.

Area of square

=(√a²+b²+c²)² = 136 sq. cm.

Then the option is (1) 136 square cm.