Question

A right isosceles triangle has an area of 65cm^2. What's the length of each leg to the nearest tenth of a cm.

Answer 1

Well, we know that the legs of this triangle are equal, and we know
that the area of any triangle is  (1/2)(base)(height) .

Since this is a right triangle, we can set it down on one leg, and then
the other leg will be the height.  Then ...

    Area = (1/2) (base) (height)

             = (1/2) (leg) (leg)

    65 cm²  =  (1/2) (leg)²

Multiply each side by  2 :  130 cm²  =  (leg)²

Take the square root of each side:      leg = √130 cm²  =  11.402 cm

                                        rounded to the nearest tenth:    11.4 cm