3. The sum of length, breadth and height of a cuboid is 12 cm. The len

1.	3. The sum of length, breadth and height of a cuboid is 12 cm. The length of the diagonal is5√2 cm. Find the surface area of the cuboid.
Answer» Answer: 94 cm² Step-by-step EXPLANATION: Let the length, breadth and height of the cuboid be l, b and h respectively. A.T.Q. Sum of length, breadth and height = 12 cm l + b + h = 12 ...(i) Also, Diagonal of cuboid = 5√2 cm ${\sf{ {\sqrt{l^2 + b^2 + h^2}} }}$ = 5√2 ...(ii) On further solving (ii), we get → ${\sf{ {\sqrt{l^2 + b^2 + h^2}} }}$ = 5√2 → l² + b² + h² = (5√2)² → l² + b² + h² = 50 ...(III) Now, Squaring both sides of (i), we get → (l + b + h)² = (12)² • { Identity : (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca } Here, a = l, b = b, c = h → l² + b² + h² + 2lb + 2bh + 2hl = 144 → l² + b² + h² + 2(lb + bh + HL) = 144 → 50 + 2(lb + bh + hl) = 144 → 2(lb + bh + hl) = 144 - 50 → 2(lb + bh + hl) = 94 As we know that, Surface AREA of cuboid = 2(lb + bh + hl), where l, b and h are length, breath and height respectively. Therefore, Surface Area of cuboid = 94 cm²

3. The sum of length, breadth and height of a cuboid is 12 cm. The length of the diagonal is5√2 cm. Find the surface area of the cuboid.

Answer»

94 cm²

Let the length, breadth and height of the cuboid be l, b and h respectively.

A.T.Q.

Sum of length, breadth and height = 12 cm

l + b + h = 12 ...(i)

Also,

Diagonal of cuboid = 5√2 cm

${\sf{ {\sqrt{l^2 + b^2 + h^2}} }}$ = 5√2 ...(ii)

On further solving (ii), we get

→ ${\sf{ {\sqrt{l^2 + b^2 + h^2}} }}$ = 5√2

→ l² + b² + h² = (5√2)²

→ l² + b² + h² = 50 ...(III)

Now,

Squaring both sides of (i), we get

→ (l + b + h)² = (12)²

• { Identity : (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca }

Here, a = l, b = b, c = h

→ l² + b² + h² + 2lb + 2bh + 2hl = 144

→ l² + b² + h² + 2(lb + bh + HL) = 144

→ 50 + 2(lb + bh + hl) = 144

→ 2(lb + bh + hl) = 144 - 50

→ 2(lb + bh + hl) = 94

As we know that,

Surface AREA of cuboid = 2(lb + bh + hl), where l, b and h are length, breath and height respectively.