Question

The length and width of a rectangle are in the ratio of $3:4$. If the rectangle has an area of $300c{m}^2$, what is the length of the diagonal?

• A. $15cm$
• B. $12cm$
• C. $25m$
• D. $25cm$

Answer 1

The correct option is D $25cm$

The length and width of the rectangle are in a ratio 3:4, so the sides can be written as 3x and 4x.
So, Area = $\left(3x\right).\left(4x\right)=300$
$12x^2=300$
$x^2=\frac{300}{12}$
$x^2=25$
$x=5$
Then length $=3x=3\times 5=15cm$
width $=4x=4\times 5=20cm$
Diagonal length of a rectangle $=\sqrt{l^2+w^2}$
$=\sqrt{{15}^2+{20}^2}$
$=\sqrt{225+400}$
$=\sqrt{625}$
$=25cm$