Question

A triangle and parallelogram have the same base and the same area if the sides of the triangle are 26 cm and 28 cm and 37 cm and the Parallelogram stands on the base 28 cm ..find the height of the parallelogram..

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Answer 1

Answer:

Here I am taking one side 30 cm instead of 37 cm . You can solve the question by putting 37 in the place of 30 .

Step-by-step explanation:

For ∆ABE, a = 30 cm, b = 26 cm, c = 28 cm

Semi Perimeter: (s) = Perimeter/2

s = (a + b + c)/2

= (30 + 26 + 28)/2

= 84/2

= 42 cm

By using Heron’s formula,

Area of a ΔABE = √s(s - a)(s - b)(s - c)

= √42(42 - 30)(42 - 28)(42 - 26)

= √42 × 12 × 14 × 16

= 336 cm2

Area of parallelogram ABCD = Area of ΔABE (given)

Base × Height = 336 cm2

28 cm × Height = 336 cm2

On rearranging, we get

Height = 336/28 cm = 12 cm

Thus, height of the parallelogram is 12 cm

Hope it helps you ◉‿◉