SOLUTION: A triangle has sides of lengths 4, 5, and 6. Find the length of altitude to the side of length 6.

Algebra ->  Pythagorean-theorem -> SOLUTION: A triangle has sides of lengths 4, 5, and 6. Find the length of altitude to the side of length 6.      Log On


   

Question 1071473: A triangle has sides of
lengths 4, 5, and 6.
Find the length of altitude to
the side of length 6.
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
The 6 unit side on the bottom, horizontally
Drawn altitude;
Left right triangle altitude y, hyptoenuse 5, leg 6-x;
Right right triangle, altitude y, hypotenuse 4, leg x;

Left and Right triangles give system%28%286-x%29%5E2%2By%5E2=25%2Cx%5E2%2By%5E2=16%29

Finding y^2 from both equations and equating:
25-%286-x%29%5E2=16-x%5E2
solving for x gives x=9%2F4.

Using x=9/4 in y^2+x^2=16,
.
y%5E2%2B%289%2F4%29%5E2=16
.
.
highlight%28y=%285%2F4%29sqrt%287%29%29-------the altitude.