Question

The sum of length breadth and height of a cuboid is 19 cm length of it's diagonal is 11cm find the surface area of the cuboid

Answer 1

Answer:

240 cm^2

Step-by-step explanation:

L + B + H = 19 cm - eq1

L^2 + B^2 + H^2 = 11^2

L^2 + B^2 + H^2 = 121 cm^2 eq2

Squaring eq1

(L + B+H)^2 = 19^2 cm^2

(L+B)^2 + H^2 + 2(L+B)H = 361

L^2 + B^2 + 2LB + H^2 + 2LH + 2BH = 361

L^2 + B^2 + H^2 + 2LB + 2LH + 2BH = 361

Putting value from eq2

121 + 2(LB + LH + BH) = 361

2(LB + LH + BH) = 240 eq 3

Surface area of cuboid = 2(LB + LH + BH)

From eq 3

2(LB + LH + BH) = 240 cm^2

Answer 2

$\fbox{\LARGE{\underline{\underline{\blue{\bf{❥Question࿐}}}}}}$

Q. The sum of length breadth and height of a cuboid is 19 cm length of it's diagonal is 11cm find the surface area of the cuboid.

$\fbox{\LARGE{\underline{\underline{\purple{\bf{❥Solution࿐}}}}}}$

$\huge\pink{✎Given,}$

$\orange{➢ l\:+b\:+h\:=\:19\:cm}$

And,

$= > \sqrt{l {}^{2} + b {}^{2} + h {}^{2} } = 11 \\ = > \: \: \: l {}^{2} + b {}^{2} + h {}^{2} = 11 {}^{2}$

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

$\huge\pink{✎Required\:to\:find:}$

$\orange{✮Surface\: area \:of \:the\: cuboid \:➫ \:2(l.b + b.h + h.l)}$

Since,

(l + b + h)² = l² + b² + h² + 2(lb + bh + hl)

$= > 19 {}^{2} = 121 + 2(lb + bh + hl) \\ = > 361 = 121 + 2(lb + bh + hl)$

$\red{➢Surface\:Area\:➫\:2(lb+bh+hl)}$

$\red{\: \: \: \: \: \: \: \:\: \:➫\:(361–121)\:cm²)}$

$\red{\: \: \: \: \: \: \: \:\: \: ➫\:240\:cm²}$

★ Hence, Surface area of

Cuboid is 240 cm²

$\huge\green{✎﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏}$

$\huge\blue{Thank\:You.!}$