SOLUTION: An isosceles triangle has a base of 10 and legs of 13. Another isosceles triangle has legs of length 13, but has a different base. The triangles have the same area. What is the len

Algebra ->  Triangles -> SOLUTION: An isosceles triangle has a base of 10 and legs of 13. Another isosceles triangle has legs of length 13, but has a different base. The triangles have the same area. What is the len      Log On


   

Question 715071: An isosceles triangle has a base of 10 and legs of 13. Another isosceles triangle has legs of length 13, but has a different base. The triangles have the same area. What is the length of the base of the second triangle?
I found the area of the first triangle by splitting it in half and using the Pythagoreum theorem to find the height.
5^2+h^2=13^2
25+h^2=169
H^2=144
H=12
1/2(10)(12)=60
Where do I go from here?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the other triangle will also be the height, h, times half of the base, a.
The altitude to the base will also divide the second triangle into two right triangles with legs a and h, and hypotenuse 13.
From the area we know ah=60
From Pythagoras we know a%5E2%2Bh%5E2=169
%28a%2Bh%29%5E2=a%5E3%2Bh%5E2%2B2%2Aah=169%2B2%2A60=169-120=289
%28a%2Bh%29%5E2=289 --> a%2Bh=sqrt%28289%29=17
From system%28a%2Bh=17%2Cah=60%29 we get
a=5 with h=12, or
a=12 with h=5.
The first option is the original triangle, so
the second triangle has h=5 and half of the base is a=12.
So the length of the base of the second triangle is
2a=2%2A12=highlight%2824%29