A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Given

The parallelogram and triangle have equal areas.

The sides of the triangle are given as 26 cm, 28 cm and 30 cm.

Using Heron’s formula, area of the triangle =[latex]\sqrt{s(s-a)(s-b)(s-c)}[/latex]

So, the perimeter = 26+28+30 = 84 cm

And its semi perimeter =s= 84/2 cm = 42 cm

= √[42(42-26)(42-28)(42-30)] cm2

= √[42×16×14×12] cm2

= 336 cm2

Let the height of parallelogram be h.

As the area of parallelogram = area of the triangle,

28 cm× h = 336 cm2

∴ h = 336/28 cm

Answer

The height of the parallelogram is 12 cm.

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