Question

the area of a rectangle is 135 square units. its length measures 9 units. find the length of its diagonal. round to the nearest tenth of a unit.

Explanation:

Step1: Find the width of the rectangle

We know that the area of a rectangle $A = l\times w$, where $A = 135$ and $l = 9$. So, $w=\frac{A}{l}$.
$w=\frac{135}{9}=15$

Step2: Use the Pythagorean theorem to find the diagonal

In a rectangle, if the length is $l$, the width is $w$ and the diagonal is $d$, then by the Pythagorean theorem $d=\sqrt{l^{2}+w^{2}}$. Here, $l = 9$ and $w = 15$.
$d=\sqrt{9^{2}+15^{2}}=\sqrt{81 + 225}=\sqrt{306}\approx17.5$

Answer:

$17.5$