Question

a wheelchair ramp with a length of 109 inches has a horizontal distance of 91 inches. what is the ramps vertical distance? the vertical distance of the ramp is

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the ramp, \(c = 109\) inches) and \(a\) is the horizontal distance (\(a=91\) inches), and \(b=x\) (vertical distance). So, \(x^{2}+91^{2}=109^{2}\).

Step2: Rearrange the formula to solve for \(x\)

\(x^{2}=109^{2}-91^{2}\). Using the difference of squares formula \(a^{2}-b^{2}=(a + b)(a - b)\), here \(a = 109\) and \(b = 91\). Then \(x^{2}=(109 + 91)(109-91)=(200)\times(18)=3600\).

Step3: Take the square root of both sides

\(x=\sqrt{3600}\). Since \(x>0\) (distance cannot be negative), \(x = 60\).

Answer:

\(60\)