Question

a right triangle has legs with lengths equal to 10 inches and 9x inches. its hypotenuse measures (x + 10) inches. what is the approximate value of the hypotenuse? 10 inches 10.25 inches 20.25 inches 81 inches

Explanation:

Step1: Apply Pythagorean theorem

$$(9x)^2 + 10^2=(x + 10)^2$$

Step2: Expand the equation

$$81x^2+100=x^2 + 20x+100$$

Step3: Simplify the equation

$$81x^2 - x^2-20x=0$$
$$80x^2-20x = 0$$
$$20x(4x - 1)=0$$

Step4: Solve for \(x\)

\(x = 0\) or \(4x-1=0\). Since \(x = 0\) will make side length \(9x = 0\) (not valid for a triangle), solve \(4x-1=0\) gives \(x=\frac{1}{4}\)

Step5: Calculate hypotenuse

Substitute \(x=\frac{1}{4}\) into \(x + 10\), we get \(\frac{1}{4}+10=10.25\)

Answer:

10.25 inches