SOLUTION: An isosceles riangle has a perimeter of 50 cm. The sum of the length of the base and the ehight of the triangle is 31 cm. Find the area of the triangle.
I set it up for 2a
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Question 120790This question is from textbook Algebra 2 and Trigonometry
: An isosceles riangle has a perimeter of 50 cm. The sum of the length of the base and the ehight of the triangle is 31 cm. Find the area of the triangle.
I set it up for 2a + b = 50
and b + h = 31
I have a lot of triangle formulas at my disposal, such as the area of a triangle = 1/2 bh, or Heron's formula for the area of a triangle. I know that we can also use the special formula for the area of an isosceles triangle. The quadratic formula of a squared + b squared = c squared too. But I guess I keep getting stuck with the fact that I've got 3 unknowns rather than 2, re: a, b, and h. In the other problems in the book, I generally have one linear equation, which I solve for a, then I substitute a into the quadratic equation. This one has me really stuck. All help very much appreciated.
This question is from textbook Algebra 2 and Trigonometry
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Yes, but h is a function of a and b.
h, a, and b/2 form a right triangle where a is the hypotenuse.
From above, you also know that
Now you have one quadratic equation in a to solve.
Use the quadratic formula.
There are two solutions.
Placing the values of "a" in the original equations, you get,
a[1]=17
b[1]=16
h[1]=15
Area[1]=120
a[2]=14.5
b[2]=21
h[2]=10
Area[2]=105
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