Question

the area of a rectangle is 380 square units. its length measures 20 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 formula of a rectangle is $A = l\times w$, where $A$ is the area, $l$ is the length and $w$ is the width. Given $A = 380$ and $l=20$, we can solve for $w$: $w=\frac{A}{l}=\frac{380}{20}=19$.

Step2: Use the Pythagorean theorem to find the diagonal

In a rectangle, if the length is $l = 20$, the width is $w = 19$, and the diagonal is $d$, by the Pythagorean theorem $d=\sqrt{l^{2}+w^{2}}$. Substitute $l = 20$ and $w = 19$ into the formula: $d=\sqrt{20^{2}+19^{2}}=\sqrt{400 + 361}=\sqrt{761}\approx27.6$.

Answer:

$27.6$