Question

the area of a rectangle is 99 square units. its width measures 9 units. find the length of its diagonal. round to the nearest tenth of a unit.

Explanation:

Step1: Find the length of the rectangle

The area formula of a rectangle is $A = lw$ (where $A$ is area, $l$ is length, $w$ is width). Given $A = 99$ and $w = 9$, we can solve for $l$:
$l=\frac{A}{w}=\frac{99}{9}=11$

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 $d$, by the Pythagorean theorem $d^{2}=l^{2}+w^{2}$. Substitute $l = 11$ and $w = 9$ into the formula:
$d=\sqrt{l^{2}+w^{2}}=\sqrt{11^{2}+9^{2}}=\sqrt{121 + 81}=\sqrt{202}\approx14.2$

Answer:

$14.2$