Question

use the image to answer the question. given ( l = 30 ) in., ( w = 20 ) in., ( h = 18 ) in., and ( x = 36.1 ) in., find the length of ( d ). round the answer to the nearest tenth. (1 point) in.

Explanation:

Step1: Apply Pythagorean theorem

In the right - triangle formed by \(x\), \(h\), and \(d\), the Pythagorean theorem states \(d^{2}=x^{2}+h^{2}\).

Step2: Substitute the given values

Given \(x = 36.1\) in and \(h=18\) in. Then \(d^{2}=(36.1)^{2}+18^{2}\).
First, calculate \((36.1)^{2}=36.1\times36.1 = 1303.21\) and \(18^{2}=324\).
So \(d^{2}=1303.21 + 324=1627.21\).

Step3: Solve for \(d\)

Take the square root of both sides: \(d=\sqrt{1627.21}\approx40.3\)

Answer:

\(40.3\)