Question

Jared is constructing a rectangular door for a shed. If the door, shown below, has a width of 42 in. and a diagonal support of 94 in., what is the approximate height of the door? A. 136 in. B. 84 in. C. 52 in. D. 103 in.

Answer 1

Answer:

B

Step-by-step explanation:

A rectangular door for a shed has a width of 42 in and a diagonal support of 94 in. The triangle formed by the rectangle's width (first leg), rectangle's length (second leg) and rectangle's diagonal (hypotenuse) is right triangle. By the Pythagorean theorem,

$\text{leg}_1^2+\text{leg}_1^2=\text{hypotenuse}^2.$

Thus,

$42^2+x^2=94^2,\\ \\x^2=94^2-42^2=7072,\\ \\x=\sqrt{7072}=4\sqrt{442}\approx 84\ in$