Question

The length of the base of an isosceles triangle is 2cm less than twice the length of any of its equal sides. If its perimeter is 98cm, what is its area?

Answer 1

Alright, so if the length of one of the equal sides are x, 2x-2 is the base and x+x+2x-2=98=4x-2. Adding 2 to both sides, we get 100=4x and dividing by 4 we get 25 as one of the equal sides and 48 as the base. Since we need to find the height to find the area, we can draw a line straight down the middle to form 2 right triangles, with the hypotenuse being 25 and the base being 48/2=24. Therefore, since a^2+b^2=c^2 and 24^2+b^2=25^2, we have

25^2-24^2=49=b^2. Square rooting both sides, we get b=7=height, and the base*height/2 is the area, so we get 48*7/2=168 as the area