Question

Find the length of the diagonal, whose length and width of a rectangle are in the ratio $5:12$. If the rectangle has an area of $504m^2$.

• A. $19m$
• B. $29m$
• C. $39m$
• D. $49m$

Answer 1

Answer: (C)

$39m$

The length and width of the rectangle are in a ratio $5:12$, so the sides can be written as $5x$ and $12x$.
So, Area $=\left(5x\right).\left(12x\right)=504$
$60x^2=504$
$x^2=\frac{504}{60}$
$x^2=9$
$x=3$
Then length $=5x=5\times 3=15m$
width $=12x=12\times 3=36m$
Diagonal length of a rectangle $=\sqrt{l^2+w^2}$
$=\sqrt{{15}^2+{36}^2}$
$=\sqrt{225+1296}$
$=\sqrt{1521}$
$=39m$