What is the exact area of the triangle?

Question

An isosceles triangle has a perimeter of 28 inches. The height of the triangle (from the vertex connecting the two equal sides down to the base) is sq.rt.(98) inches. What is the exact area of the triangle 

Answer 1

Suggestion: DRAW THIS TRIANGLE and LABEL all the facts that you know about it.

 

The altitude (height) creates 2 right ∇s; in each one the hypotenuse is 14-x, x is the base, and the altitude (other leg) is 7√2 (Verify this by adding two sides, 14-x each, plus the base, 2x, of the isosceles triangle to get perimeter = 28.

 

Now apply the Pythagorean Theorem to one of the two rt. triangles; thus you will solve for x.

 

Then the area of the isosceles triangle is ½(2x)(7√2.  Note: √98 = 7√2.