Question

geometry chapter 7 review a rectangular gate is shown below. if the gate has a height of 38.6 in, what is its width? round your answer to the nearest whole inch.

Explanation:

Step1: Recall Pythagorean theorem

For rectangle, diagonal $d$, height $h$, width $w$: $d^2 = h^2 + w^2$

Step2: Rearrange for width

$w = \sqrt{d^2 - h^2}$

Step3: Substitute given values

$d=50.8$ in, $h=38.6$ in:
$w = \sqrt{50.8^2 - 38.6^2}$

Step4: Calculate squares

$50.8^2 = 2580.64$, $38.6^2 = 1489.96$

Step5: Compute difference

$2580.64 - 1489.96 = 1090.68$

Step6: Find square root

$\sqrt{1090.68} \approx 18.97$

Step7: Round to whole number

$\approx 19$

Answer:

19 inches