Question

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelogram.

Answer 1

The sides of a triangle DCE are
DC = 15 cm, CE = 13 cm, ED = 14 cm
Let h be the height of parallelogram ABCD
Given,
Perimeter of ΔDCE

2s = DC + CE + ED

`⇒S=1/2(15+13+4)`

`⇒s=1/2(42)`

`⇒s=21cm`

𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝐷𝐶𝐸 = `sqrt(s(s-dc)(s-ce)(s-ed))`

`=sqrt(21(21-15)(21-13)(21-14))`

`=sqrt(21xx7xx8xx6)`

`=sqrt(84xx84)`

`84 cm^2`

Given that
Area of Δ𝑙𝑒 𝐷𝐶𝐸= 𝑎𝑟𝑒𝑎 𝑜𝑓 𝐴𝐵𝐶𝐷
= Area of parallelogram ABCD = =`84cm^2`
⇒ 24×ℎ=84 [∴ Area of parallelogram = base × height]
⇒ h = 6 cm