Question

5
note: figure not drawn to scale
if x is a positive integer in the right triangle above,
what is the value of x?
(the right triangle has a leg of length 12, a leg of length ( 9 - x ), and hypotenuse of length ( 9 + x ))

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(a = 12\), \(b = 9 - x\), \(c = 9 + x\). So, \(12^2+(9 - x)^2=(9 + x)^2\)

Step2: Expand the equation

\(144 + 81-18x+x^2 = 81 + 18x+x^2\)

Step3: Simplify the equation

Subtract \(x^2\) and 81 from both sides: \(144-18x=18x\)

Step4: Solve for x

Add \(18x\) to both sides: \(144 = 36x\), then \(x=\frac{144}{36}=4\)

Answer:

\(4\)