In ΔABC, ∠ABC = ∠DAC, AB = 8 cm, AC = 4 cm and AD = 5 cm. Find the area of ΔACD: area of ΔABC - Noon Academy

In ΔABC, ∠ABC = ∠DAC, AB = 8 cm, AC = 4 cm and AD = 5 cm. Find the area of ΔACD: area of ΔABC

Class 10 | Exercise 15E | ICSE | Maths | Selina | Similarity (With Applications to Maps and Models)

In ΔABC, ∠ABC = ∠DAC, AB = 8 cm, AC = 4 cm and AD = 5 cm. Find the area of ΔACD: area of ΔABC

Selina Solutions Concise Class 10 Maths Chapter 15 ex. 15(E) - 12

Solution:

As,

$\vartriangle ACD\text{ }\sim\text{ }\vartriangle BCA$

We have,

$Ar\left( \vartriangle ACD \right)/\text{ }Ar\left( \vartriangle BCA \right)$

$=\text{ }A{{D}^{2}}/\text{ }A{{B}^{2}}~=\text{ }{{5}^{2}}/{{8}^{2}}$

So,

$Ar\left( \vartriangle ACD \right)/\text{ }Ar\left( \vartriangle BCA \right)$

$=\text{ }25/64$

i

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