Answer: a) base = 1 ft b) height = 4 ft
Step-by-step explanation:
Set this up as a right triangle where base = x, height = 2x + 2, and hypotenuse (length of the ladder) = 13
Use Pythagorean Theorem to create a quadratic equation, factor, then apply the Zero Product Property to solve for x.
(x)² + (2x + 2)² = 13²
x² + 4x² + 8x + 4 = 169
5x² + 8x - 165 = 0
(5x + 13) (x - 1) = 0
x = -13/5 x = 1
We know that distance cannot be negative so disregard x = -13/5.
The only valid answer is x = 1
base = x --> x = 1
height = 2x + 2 --> 2(1) + 2 = 4
