Question

The perimeter of a cuboid is 320 m and the ratio of its dimensions is 5:2:1. Find its lateral surface area

Answer 1

Dimensions of a cuboid are in the ratio=5:3:1

∴ length=l=5x

Breadth=b=3x and height=h=x

Total surface area of a cuboid=2(lb+bh+lh)

⇒414=2(5x×3x+3x×x+5x×x)

⇒414=2(15x

2

+3x

2

+5x

2

)

⇒414=2×23x

2

⇒207=23x

2

⇒x

2

=

23

207

=9

∴x=

9

=3

∴ Length=5x=5×3=15m

Breadth=3x=3×3=9m

and height=h=x=3m

Answer 2

Given:

We have perimeter of cuboid is 320m. are ratio of dimention 5:2:1

To Find:

We need to find the lateral suface area of cuboid?

Step-by-step explanation:

• Sicne we have ratios of the dimension of cuboid id 5:2:1

• Then let the dimension of the cuboid be 5x,2x,x

• Hence, we can write Length of cuboid, l=5x

• breadth of cuboid, b =2x

• Heigth of cuboid,h=x

• Thus we know perimeter of cuboid is given the formula

                  $=2(lb+bh+hl)$

• we have perimeter of cuboid is 320 and length=5x, breadth =2x, height =x put it in above equation we get

               $320=2(5x\times2x+2x\times x+x\times5x)$

• Solve the above equation we get

                    $320=2(10x^2+2x^2+5x^2)\\320=34x^2\\x^2=\frac{320}{34} \\x=\sqrt{\frac{160}{17} }$

Thus, length of cuboid will be 5x=$5\sqrt{\frac{160}{17} }$

        Breadth of cuboid will be 2x=$2\sqrt{\frac{160}{17} }$

         Height of cuboid will be x=$\sqrt{\frac{160}{17} }$