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 = [tex]\frac{-2}{3}+\frac{\sqrt{193} }3\\[/tex]
h = 11.89/3
h = 3.96 units
Hence the height of the triangle if the base is 8 is 3.96 units
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