Question

The sum of the length, breadth and depth of a
cuboid is 19 cm and its diagonal is 5 5 cm. It
surface area is:

Answer 1

$\large\underline\orange{\tt CorrectQuestion :-}$

★ The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5√5 Cm. Its surface area is:

Given:

• Sum of Length , Breadth and Depth of rectangle is 19 cm
• Length of diagonal is 5√5 cm

To Find:

• Surface area of Cuboid

Solution: Let length , breadth and height of Cuboid be l , b and h respectively.

• l + b + h = 19 cm ( given )

★ We know that diagonal of Cuboid =√l² + b² + h² ★

• √l² + b² + h² = 5√5 ( given )

$\small\implies{\sf }$ l² + b² + h² = 125

★ TSA of Cuboid = 2 (lb + bh + hl ) ★

A/q,

• Take l + b + h = 19

Squaring on both the sides

$\small\implies{\sf }$ ( l + b + h )² = 19²

• Since, (a+b+c)² = a² + b² + c² +2(ab+bc+ca)

$\small\implies{\sf }$ l² + b² + h² + 2(lb + bh + hl ) = 361

$\small\implies{\sf }$ 125 + T.S.A = 361

$\small\implies{\sf }$ T.S.A = 361 – 125

$\small\implies{\sf }$ T.S.A = 236 cm²

Hence, Cuboid's surface area will be 236 cm²