Question

the area of a rectangle is 105 square units. its width measures 7 units. find the length of its diagonal. round to the nearest tenth of a unit.

Explanation:

Step1: Find the length of the rectangle

We know that the area of a rectangle $A = l\times w$. Given $A = 105$ and $w = 7$. So, $l=\frac{A}{w}=\frac{105}{7}=15$.

Step2: Use the Pythagorean theorem to find the diagonal

In a rectangle, if the length is $l = 15$, the width is $w = 7$, and the diagonal is $d$. By the Pythagorean theorem $d=\sqrt{l^{2}+w^{2}}$. Substitute $l = 15$ and $w = 7$ into the formula: $d=\sqrt{15^{2}+7^{2}}=\sqrt{225 + 49}=\sqrt{274}\approx16.6$.

Answer:

$16.6$