Question

Question 4
A Triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26cm, 28cm and 30cm,and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Answer 1

For triangle
Perimeter of triangle =(26 + 28 +30)cm = 84 cm
2s =84cm
s =42cm
By Heron’s formula,
Area of the triangle = $\sqrt{s(s-a)(s-b)(s-c)}$
= $\lfloor \sqrt{42(42-26)(42-28)(42-30)}\rfloor c{m}^2=\lfloor \sqrt{\left(42\right)\left(16\right)\left(14\right)\left(12\right)}\rfloor c{m}^2=336c{m}^2$
Let the height of the parallelogram be h. Area of parallelogram = Area of triangle
$h\times 28cm=336c{m}^2$
$h=12cm$
Therefore, the height of the parallelogram is 12 cm.