Question

1. solve for x. round to the nearest tenth.

x =

Explanation:

Step1: Use the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. In this case, \(x\) is one of the legs, \(a = 29\), \(c=x + 12\). So we have \(29^{2}+x^{2}=(x + 12)^{2}\).

Step2: Expand the equation

Expand \((x + 12)^{2}\) using the formula \((a + b)^{2}=a^{2}+2ab + b^{2}\). So \((x + 12)^{2}=x^{2}+24x+144\). The equation becomes \(841+x^{2}=x^{2}+24x + 144\).

Step3: Simplify the equation

Subtract \(x^{2}\) from both sides of the equation. We get \(841=24x+144\).

Step4: Solve for \(x\)

First, subtract 144 from both sides: \(841-144 = 24x\), so \(697=24x\). Then \(x=\frac{697}{24}\approx29.0\).

Answer:

\(29.0\)