Question

1. a wheelchair ramp is 10 feet long. the ramp sits up on a 2 - foot platform. how far is it from the end of the ramp to the bottom of the platform?

a² + b² = c²
a²+2² = 10²
a² + 4 = 100
100 + 4 = 104
√104

Explanation:

Step1: Apply Pythagorean theorem

The ramp, the vertical height of the platform and the distance from the end of the ramp to the bottom - of the platform form a right - triangle. The length of the ramp is the hypotenuse $c = 10$ feet and the height of the platform is one of the legs $b = 2$ feet. Let the distance we want to find be $a$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, so $a^{2}+2^{2}=10^{2}$.

Step2: Simplify the equation

$a^{2}+4 = 100$. Then, subtract 4 from both sides of the equation: $a^{2}=100 - 4$.

Step3: Solve for $a$

$a^{2}=96$. Take the square root of both sides. Since $a$ represents a distance, we take the positive square root. $a=\sqrt{96}=4\sqrt{6}\approx9.8$ feet.

Answer:

$4\sqrt{6}\approx9.8$ feet