Question

The length, breadth and height of a rectangular solid are in the ratio $5:4:2$. If the total surface area is $1216c{m}^2,$ find the length, the breadth and the height of the solid.

• A. $20cm,16cm$ and $8cm$
• B. $10cm,16cm$ and $8cm$
• C. $10cm,8cm$ and $2cm$
• D. $15cm,12cm$ and $6cm$

Answer 1

The correct option is A $20cm,16cm$ and $8cm$

Let $l=5x,b=4x$ and $h=2x$

S.A. $=2(20x^2+8x^2+10x^2)$

$2\left(38x^2\right)=1216$

$x=\sqrt{\frac{1216}{76}}$

$x=\sqrt{16}=4$

$l=20cm$

$b=16cm$

$h=8cm$