Question

The sum of lenhth breadth and height of a cuboidal room is 26 m and the length of its diagonal is 20 m find the total surface area of cuboid

Answer 1

$\huge\underline{\bold{\red{Answer\::}}}$

A.T.Q

Sum of length, breadth, and height of a cuboidal room is 26m

l + b + h = 26m ___(1)

And length of it's diagonal is 20m


$\sqrt{ {l}^{2} \: + \: {b}^{2} + \: {h}^{2}}$ = 20

Squaring on both sides we get

l² + b² + h² = (20)²

We have to find total surface area of Cuboid.

Means;

2 (lb + bh + hl) = ?

l² + b² + h² = (20)²

(l + b + h)² - 2(lb + bh + hl) = 400

(26)² - 2(lb + bh + hl) = 400 [from (1)]

676 - 2(lb + bh + hl) = 400

676 - 400 = 2(lb + bh + hl)

276 = 2(lb + bh + hl)

2(lb + bh + hl) = 276

$\textbf{So, the total surface area of Cuboid is}$ $\textbf\red{276}$ $\textbf\red{{m}^{2}}$

Answer 2

A.T.Q

Sum of length, breadth, and height of a cuboidal room is 26m

l + b + h = 26m ___(1)

And length of it's diagonal is 20m

\sqrt{ {l}^{2} \: + \: {b}^{2} + \: {h}^{2}}

l

2

+b

2

+h

2

= 20

Squaring on both sides we get

l² + b² + h² = (20)²

We have to find total surface area of Cuboid.

Means;

2 (lb + bh + hl) = ?

l² + b² + h² = (20)²

(l + b + h)² - 2(lb + bh + hl) = 400

(26)² - 2(lb + bh + hl) = 400 [from (1)]

676 - 2(lb + bh + hl) = 400

676 - 400 = 2(lb + bh + hl)

276 = 2(lb + bh + hl)

2(lb + bh + hl) = 276