A triangle and a parallelogram have the same base and the same area If the sides of the triangle are - Maths - Heron\s Formula

Question

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

Ajanta Trivedi · Accepted Answer

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

therefore using heron's formula to calculate the area of the triangle

$A = \sqrt{s (s - a) (s - b) (s - c)}$ where A is the area of the triangle with sides a , b and c. and s be the semi perimeter

s = (a+b+c) / 2

$s = \frac{26 + 28 + 30}{2} = \frac{84}{2} = 42$

area of the triangle

$= \sqrt{42 (42 - 26) (42 - 28) (42 - 30)} = \sqrt{42 * 16 * 14 * 12} = \sqrt{2 * 3 * 7 * 4^{2} * 2 * 7 * 2^{2} * 3} = 2 * 4 * 2 * 3 * 7 = 336 c m^{2}$

area of the parallelogram = area of the triangle

area of the parallelogram = base *height

therefore

$28 h = 336$ where h is the height of the parallelogram

$h = \frac{336}{28} = 12 c m$

thus the height of the parallelogram is 12 cm.

hope this helps you.

cheers!!

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