Question

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.​

Answer 1

Given:-

the parallelogram and the triangle have equal areas

the parallelogram and the triangle have equal areasThe sides of the triangle are given as 26 cm, 28 cm and 30 cm.

the perimeter = 26+28+30 = 84 cm

And its semi perimeter $= \frac{84}{2} cm = 42$

Now, by using Heron’s formula, area of the triangle

$= \sqrt{s(s - a)(s - b)(s - c)}$

$= √[42(42-26)(42-28)(42-30)] cm²$

$= √[42×16×14×12] cm²$

$= 336 cm²$

Now, let the height of parallelogram be h.

As the area of parallelogram = area of the triangle,

$28 cm× h = 336 cm²$

$∴ h = \frac{336}{28 }$

So, the height of the parallelogram is 12 cm.

Hope it helps