In the given figure, the ratio AD to DC is 3 to 2. If the area of Δ ABC is 40 cm2, what is the area of Δ BDC? - Mathematics

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Answer in Brief

In the given figure, the ratio AD to DC is 3 to 2. If the area of Δ ABC is 40 cm2, what is the area of Δ BDC?

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Solution

Area of triangle ABC is given 40 cm2.

Also `AD : DC = 3:2`

We are asked to find the area of the triangle BDC

Let us take BE perpendicular to base AC in triangle ABC.

We assume AC equal to y and BE equal to x in triangle ABC

Area of triangle ABC, say A is given by

`A = 1/2 ` ( Base × Height)

`40 = 1/2 (AC xx BE )` 

`40 = 1/2 ( y xx x)`

`xy = 40 xx 2`

xy = 80

We are given the ratio between AD to DC equal to 3:2

So,

`AD = 3/5 y`

`DC = 2/5 y`

In triangle BDC, we take BE as the height of the triangle

Area of triangle BDC, say A1 is given by

`A_1 = 1/2 `( Base × Height ) 

`A_1 = 1/2 ( DC xx BE ) `

`A_1 = 1/2 (2/5y xx x)`

`A_1 = 1/5 xy `

`A_1 = 1/5 xx 80 ( as xy = 80 ) `

`A_1 = 16   cm^2`

 

 

Concept: Application of Heron’s Formula in Finding Areas of Quadrilaterals
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.4 | Q 12 | Page 25

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