Question

ABC is a triangle in which ∠A = 90°, AN ⊥ BC, BC = 12 cm and AC = 5 cm. Find the ratio of the area of ∆ANC and ∆ABC.

Answer 1

SOLUTION :  

Given:

In ΔABC, ∠A=90∘, AN ⊥ BC, BC= 12 cm and AC = 5 cm.

In ΔANC and ΔABC,

∠ACN=∠ACB   (Common)

∠A=∠ANC     (each 90°)

ΔANC ∼ΔABC (By AA similarity)

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

Therefore,

ar(ΔANC)/ar(ΔABC) = (AC/BC)²

ar(ΔANC)/ar(ΔABC) = (5/12)²

ar(ΔANC)/ar(ΔABC) = 25/144

Hence,the ratio of the area of  ΔANC and  ΔABC is 25 : 144.

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Answer 2

$\huge{hello dear }$

$<b><i><u>your answer is attachment </b></i></u>$

➡ratio➡25:144
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