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A Triangle and a Parallelogram Have the Same Base and the Same Area. If the Sides of the Triangle Are 13 Cm, - Mathematics

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.

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Solution

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`

π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ Δ𝐷𝐢𝐸 = `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 𝐷𝐢𝐸= π‘Žπ‘Ÿπ‘’π‘Ž π‘œπ‘“ 𝐴𝐡𝐢𝐷
= Area of parallelogram ABCD = =`84cm^2`
⇒ 24×β„Ž=84 [∴ Area of parallelogram = base × height]
⇒ h = 6 cm

Concept: Area of a Triangle by Heron's Formula
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.2 | Q 11 | Page 20
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