The length of the hypotenuse of a right triangle is one unit more than twice the height. What is the height of the triangle if t

Question

3 years ago

5

he base is 8?

1 answer:

lisabon 2012 [21] · Answer 1 · 2022-10-17T20:12:46+03:00

The height of the triangle if the base is 8 is 3.96 units

Given the following parameters

Base of a triangle = 8 units

Let the hypotenuse be "c"

Let the height be "h"

If the length of the hypotenuse of a right triangle is one unit more than twice the height, then;

c = 2h + 1

According to the Pythagoras theorem:

c² = b² + h²

(2h + 1)² = 8² + h²

Expand

4h²+4h+1 = 64 + h²

4h²-h² + 4h + 1 - 64 = 0

3h² + 4h - 63 = 0

Factorize the result

On factorizing, the value of the height is 2

h = $\frac{-2}{3}+\frac{\sqrt{193} }3\\$

h = 11.89/3

h = 3.96 units

Hence the height of the triangle if the base is 8 is 3.96 units