Question

the sum of the length ,breadth,depth of a cuboid is 19cm and the length of its diagonal is 11cm. find the surface area of the cuboid

Answer 1

361 - s.a = 121
therefore s.a of cuboid = 240 sq.cm

Answer 2

Answer:

Let the length, breadth and depth of the cube be l cm, b cm and h cm respectively. Then,

•$\sf\qquad{l+b+h=19}$

Now,

•$\sf\qquad{Diagonal=11cm}$

$\implies$ $\sf\sqrt{l^2+b^2+h^2}=11$

$\sf{l^2+b^2+h^2=121}$

Now,

$\leadsto$$\sf\qquad{l+b+h=19}$

$\leadsto$$\sf\qquad{(l+b+h)^2=19^2}$

$\leadsto$$\sf\qquad{l^2+b^2+h^2+2(lb+bh+hl)=361}$

$\leadsto$$\sf\qquad{121+2(lb+bh+hl)=361}$

$\leadsto$$\sf\qquad{2(lb+bh+hl)=240}$

Hence, the surface area of the cuboid is 240 cm².