SOLUTION: Given the isosceles triangle ACB (right angle C) with sides of length 6, a) find the altitude CD ( point D is between line AB b) find the area of triangle ACB.

Algebra ->  Triangles -> SOLUTION: Given the isosceles triangle ACB (right angle C) with sides of length 6, a) find the altitude CD ( point D is between line AB b) find the area of triangle ACB.      Log On


   

Question 779100: Given the isosceles triangle ACB (right angle C) with sides of length 6, a) find the altitude CD ( point D is between line AB b) find the area of triangle ACB.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You mean, with LEGS of length 6. This is a Special triangle, 45-45-90 Degreed. The area is simply, taken one leg as a base, AREA RESULT: %281%2F2%296%2A6=highlight%2818%29 square units.

Knowing the area, and leg lengths permit you to find the altitude. First you can find the longest side, which could act as a base. Use pythagorean theorem to find this base (which is hypotenuse of the right-isosceles triangle):

b%5E2=6%5E2%2B6%5E2
b=sqrt%2836%2B36%29
b=sqrt%2872%29
b=sqrt%282%2A2%2A3%2A2%2A3%29
b=6%2Asqrt%282%29

Let A = area of 18
Let b = base of 6*sqrt(2)
Let a = altitude, unknown to be found

Area Formula: %281%2F2%29ba=A
a=2A%2Fb
Substitute the known values:
highlight%28a=2%2A18%2F%286%2Asqrt%282%29%29%29
a=6%2Fsqrt%282%29
a=%286%2F2%29sqrt%282%29
FINAL RESULT: highlight%28a=3sqrt%282%29%29