What is the height of the triangle if its base is 2 times its height?

Question

the ratio of the area of a triangle to the area of a rectangle is 3:5.the difference in their areas is 54 square inches

Answer 1

let the base = b

    the height =h

base is 2 times its height b = 2h

area of a triangle =bh/2

substitute b = 2h ,h =h in the formula

                 =(2h*h) / 2

cancel common factor

                   =h^2

the ratio of the area of a triangle to the area of a rectangle is = 3:5

                       .the difference in their areas is  = 54 square inches

                     the difference in their areas ratios =5 -3 =2 parts

                                                            2 parts =54

                                                            1 part =27

        the area of a triangle ( 3parts) =27 *3

                                                   =81square inches

                                                h^2=81

                                                h^2 =9^2

                                                h =9

the solution is h =  9 inches