Question

the sum of length breadth and height of a cuboid is 21cm and the length of the diagnol is 12cm find the surface area of the cuboid​

Answer 1

The surface area of the cuboid is 297 cm²

Step-by-step explanation:

we have to find the surface area of the cuboid

surface area of cuboid = 2(lb+bh+hl)

where l,b,h are the length , breadth and height of the cuboid .

given that ,

sum of length breadth and height of a cuboid is 21cm

i.e l+b+h = 21 cm ...(1)

and diagonal = 12 cm

diagonal of a cuboid  d= $\sqrt{l^2+b^2+h^2}$

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

squaring both sides

144 = l²+b²+h²...(2)

taking

(l+b+h)² = l²+b²+h²+2lb+2bh+2hl

using eq (1) and (2)

(21)² =  144 + 2(lb+bh+hl)

441 = 144 + 2(lb+bh+hl)

441-144 =  2(lb+bh+hl)

297 =2(lb+bh+hl)

surfce area of the cuboid is  2(lb+bh+hl)

hence , The surface area of the cuboid is 297 cm²

#Learn more:

The sum of length, breadth and height of a cuboid is 19 cm and the length of its diagnol is 11 cm. Find the surface area of the cuboid.

https://brainly.in/question/993412

Answer 2

Answer:

The surface area of the cuboid is 297 cm²

Step-by-step explanation:

we have to find the surface area of the cuboid

surface area of cuboid = 2(lb+bh+hl)

where l,b,h are the length , breadth and height of the cuboid .

given that ,

sum of length breadth and height of a cuboid is 21cm

i.e l+b+h = 21 cm ...(1)

and diagonal = 12 cm

diagonal of a cuboid  d= \sqrt{l^2+b^2+h^2}l2+b2+h2

12 = \sqrt{l^2+b^2+h^2}l2+b2+h2

squaring both sides

144 = l²+b²+h²...(2)

taking

(l+b+h)² = l²+b²+h²+2lb+2bh+2hl

using eq (1) and (2)

(21)² =  144 + 2(lb+bh+hl)

441 = 144 + 2(lb+bh+hl)

441-144 =  2(lb+bh+hl)

297 =2(lb+bh+hl)

surfce area of the cuboid is  2(lb+bh+hl)

hence , The surface area of the cuboid is 297 cm²