Question

a triangle and parallelogram have the same base and area if the sides of triangle are 9,12,15, cm and the parallelogram stands on the base 9 cm find the height of parallelogram​

Answer 1

Given :-

Base of the ||gm = 9 cm

Sides of the triangle = 9 cm , 12 cm and 15 cm

Area of the triangle , by herons formula since it's all three sides are given :-

S = Sum of all three Sides / 2

S = (9 + 12 + 15 )/ 2 = 36/2 = 18

| gmArea = √ S(S - a)(S - b)(S - c)

=> √18(18 - 9)(18 - 12)(18 - 15)

=> √18(9)(6)(3)

=> √2 x 3 x 3 x 3 x 3 x 2 x 3 x 3

=> 2 x 3 x 3 x 3

=> 54 cm²

Now , according to the question

Area of ||gm = Area of ∆

So , base x height = 54

[ Area of ||gm = base x height ]

9 x height = 54

height = 54/9

height = 6 cm

Hence height of the ||gm is 6 cm

HOPE IT HELPED ...