Question

pythagorean unit practice
possible points: 4.35
the width of a rectangle is 4 feet, and the diagonal length of the rectangle is 13 feet. which measurement is closest to the length of this rectangle in feet?
a 9 ft
b 13.6 ft
c 17 ft
d 12.4 ft

Explanation:

Step1: Apply Pythagorean theorem

In a rectangle, if the width is $w = 4$ feet, the length is $l$, and the diagonal is $d=13$ feet. According to the Pythagorean theorem $w^{2}+l^{2}=d^{2}$. So, $l^{2}=d^{2}-w^{2}$.

Step2: Substitute values

Substitute $w = 4$ and $d = 13$ into the formula: $l^{2}=13^{2}-4^{2}=169 - 16=153$.

Step3: Calculate the length

$l=\sqrt{153}\approx12.369$.

Answer:

D. 12.4 ft