SOLUTION: Can someone assist with this problem? PLEASE? I have a triangle, divided into two triangles. I have to figure out the area of the entire one triangle as a whole. The left side o

Algebra ->  Surface-area -> SOLUTION: Can someone assist with this problem? PLEASE? I have a triangle, divided into two triangles. I have to figure out the area of the entire one triangle as a whole. The left side o      Log On


   

Question 706561: Can someone assist with this problem? PLEASE?
I have a triangle, divided into two triangles. I have to figure out the area of the entire one triangle as a whole. The left side of the triangle has a length of 10 meters, and it gives two base lengths, one is 8 meters of the one triangle on the left, and the other base length is 15 meters, with no additional info. given, please help solve.
Thankyou.
Answer by Edwin Parker(36) About Me  (Show Source):
You can put this solution on YOUR website!
It can be worked if the triangle on the left is isosceles,
like this:



 matrix%286%2C1%2C%0D%0A%0D%0Aor%2C+a%2C+right%2Ctriangle%2Clike%2C%22this--%3E%22%29 

If it's the first case, we draw the height, h, or altitude (in green), and
dividing the 8 base into two segments 4 each

   

In either case we use the Pythagorean theorem to get the height h

4˛ + h˛ = 10˛                                 8˛ + h˛ = 10˛
16 + h˛ = 100                                 64 + h˛ = 100
     h˛ = 84                                       h˛ = 36
      h = √84                                       h = √36
      h = √4*21                                     h = 6
      h = 2√21

The formula for the area of a triangle is A = 1%2F2base×height

We have the base in both cases as 8+15 or 23.

The case on the left is 

A = 1%2F2(23)2√21
  = 23√21
  = 105.4 square meters, approximately

On the right,

A = 1%2F2(23)(6) 
  = 69 square meters

Edwin