Question

If a right isosceles triangle has an area of 192 cm, what is the height of the triangle?

Answer 1

The height of the triangle is 19.596 centimeter, if a right isosceles triangle has an area of 192 square centimeters.

Step-by-step explanation:

The given is,

               Area of right isosceles triangle is 192 square centimeters

Step:1

             Formula for area of  right isosceles triangle is,

                                       $A=\frac{1}{2} a^{2}$............................(1)

            Where, a - Sides of triangle

                         a = h = b

            Here, h - Height of triangle

                      b - Base of triangle

           From given,

                    Area, A = 192 square centimeters

           Equation (1) becomes.

                              $192=\frac{1}{2} a^{2}$

                                $a^{2} = (2)(192)$

                                     = 384

                                $a^{2} = 384$

          Take square root on both sides,

                                 $a=\sqrt{384}$

                                  a = 19.596 centimeters

         Height of right isosceles of triangle, a = h = 19.596 centimeters

Result:

        The height of the triangle is 19.596 centimeter, if a right isosceles triangle has an area of 192 square centimeters.