Question

The total area of four walls of a room is $108$ square meters. The length and height of the room are in the ratio $5:2$ and the height and width are in the ratio $4:5$. What is the floor area of the room?

Answer 1

Given:
Length $\left(l\right)$:height $\left(h\right)=5:2......\left(1\right)$
Height $\left(h\right)$:width $\left(w\right)=4:5......\left(2\right)$
Multiply by 2 in equation (1),
Length $\left(l\right)$:height $\left(h\right)=5\times 2:2\times 2=10:4.......\left(3\right)$
Combining equation (3) and (2), we get
$l:h:w=10:4:5$
Let length $=10x$, width $=5x$, and height $=4x.$
Given, area of the four walls of a room $=108sqm$
$\Rightarrow 2(l+w)h=108$
$\Rightarrow (l+w)h=54$
$\Rightarrow (10x+5x)4x=54$
$\Rightarrow 60x^2=54$
$\Rightarrow x^2=\frac{54}{60}$

Floor area of the room $=l\times w=10x\times 5x=50x^2$
$=50\times \frac{54}{60}=45sqm$