SOLUTION: two sides of a triangular field are of the same length 13 ft.Third side is 10ft. in length.Find the area of the field in square feet.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: two sides of a triangular field are of the same length 13 ft.Third side is 10ft. in length.Find the area of the field in square feet.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 934116: two sides of a triangular field are of the same length 13 ft.Third side is 10ft. in length.Find the area of the field in square feet.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You can use the perpendicular bisector segment to the middle of the 10 foot side to the angle opposite this 10 foot side as the height of the triangle, and the 10 foot side as the base.

That will form two right-triangles allowing for Pythagorean theorem to determine the height. One leg of each of the triangles is half of 10, or 5 feet. Each of the 13 foot sides is a hypotenuse.

If y is the height, then
y%5E2%2B5%5E2=13%5E2
y%5E2=13%5E2-5%5E2
y%5E2=169-25
highlight_green%28y=12%29

Now you want the area of the original isosceles triangle.
AREA of a triangle is highlight%28%281%2F2%2910%2A12%29; uncomputed, so you can see the use of the values in the area formula.