Question

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

Answer 1

❥${\red{\underline{\underline{\huge{\mathtt{Question:-}}}}}}$

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

❥${\red{\underline{\underline{\huge{\mathtt{Solution:-}}}}}}$

• The sum of length, breadth and height of cuboid = 19 cm.

• The length of its diagonal= 11 cm.

Consider,

• Length of cuboid = x cm.
• Breadth of cuboid = y cm.
• Height of cuboid = z cm.

We know that,

ᴥ${\blue{\boxed{\bold{Length\:of\: diagonal=\sqrt{ length^2+breadth^2+height^2}}}}}$

➪According to the question,

x+y+z = 19..............(i)

$\sqrt{ {x}^{2} + {y}^{2} + {z}^{2} } = 11 \\ = > {x}^{2} + {y}^{2} + {z}^{2} = 121...............(ii)$

★${\green{\boxed{\bold{ Surface\: area\: of\: cuboid= 2(Length× Breadth+ Breadth× Height+Length×Height}}}}$

✞ Take (i) no. equation ✞

x+y+z = 19

[Squre in both sides]

→(x+y+z)² = 19²

[ Apply the formula➪ (a+b+c)² = a² + b²+c² +2(ab+bc+ca)]

→x² + y²+z²+2(xy+yz+zx)=361

[ Put the value of x²+y²+z² = 121]

→121 + 2(xy+yz+zx) =361

→ 2(xy+yz+zx) = 240

❥${\red{\underline{\underline{\huge{\mathtt{Answer:-}}}}}}$

Hence, the surface area of cuboid is 240 cm².