Question

The length, breadth and height of a cuboid are in the ratio 7:6:5. If the surface area of the cuboid is 1926 sq. cm. The length of the diagonal of the cube is ​

Answer 1

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The length, breadth and height of a cuboid are in the ratio 7:6:5. If the surface area of the cuboid is 1926 sq. cm. The length of the diagonal of the cuboid is ​

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Given :-

Surface area of the cuboid = 1,926 sq. cm

Length = 7x

Breadth = 6x

Height = 5x

To Find :-

The length of the diagonal.

Solution :-

Surface area of the cuboid is already given as 1,926 sq.cm

As we know TSA of a cuboid = 2 (lw + wh + lh)  sq. units

Actually we don't know length , breadth & height here.

But we know that it is in the ratio,

• 7 : 6 : 5

• TSA = 2 (lw + wh + lh)

• 1,926 = 2( 7x × 6x + 6x × 5x + 5x × 7x)

• 1,926 = 2( 42x + 30x + 35x )

• 1,926 = 2( 107 x)

• 1,926 = 214 x

• 1,926 ÷ 214 = x

• x = 9

Now we got the value of 'x' as 9.

⇒ Length = 7x = 63 m

⇒ Breadth = 6x = 54 m

⇒ Height = 5x = 45 m.

We need to find the diagonal of this cuboid.

As we know,

Diagonal of a cuboid = √ ( l2 + b2 +h2)

⇒ Diagonal = √( 63 + 54 + 45)

⇒ Diagonal = √(162)

⇒ Diagonal = 12.72 cm apprx.

The required answer is 12.72 cm.