Question

the dimensions of a rectangular box are in a ratio 4:3:1 its lateral surface area is 350 cm^2 then what's the length of h in it?

Answer 1

Please mention which one of it is height ,breadth and length?

I am solving it by assuming 4:3:1 as length,breadth and height respectively.

Let the dimensions of the rectangular box be 4x cm,3x cm, and 1x cm.
Given that lateral surface area of the rectangular box=350 square cm
Lateral surface area of a rectangle=2(lh+bh)units
=2h(l+b)units
ATQ:-

$= > 350 = 2 \times 1x(4x + 3x)$

$= > 350 = 2x \times 7x$

$= > 350 = 14x {}^{2}$

$= > \frac{350}{14} = x {}^{2}$

$= > 25 = x {}^{2}$

$= > \sqrt{25} = x$

$= > 5 = x$

Now, we have the value of x (5 cm), and from that we can derive the values of the length, breadth and height of the rectangular box.

Length=4x cm
=(4×5) cm
=20 cm

Breadth=3x cm
=(3×5) cm
=15 cm

Height=1x cm
=(1×5) cm
=5 cm