ABC is a triangle in. which $∠ A = 90^{\circ}, A N ⊥ B C, B C = 12 c m$ and AC = 5 cm. Find the ratio of the areas of $Δ A N C$ and $Δ A B C$

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Solution

In ΔANC and ΔABC
∠C = ∠C [Common]
∠ANC = ∠BAC [Each 90°]
Then, ΔANC ~ ΔBAC [By AA similarity]

By area of similarity triangle theorem

$fraction numerator a r left parenthesis A N C right parenthesis over denominator a r left parenthesis B A C right parenthesis end fraction space equals space open parentheses fraction numerator A C over denominator B C end fraction close parentheses squared space equals space open parentheses 5 over 12 close parentheses squared space equals space 25 over 144$

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ΔABC is right angled at A (see the given figure). AD is perpendicular to BC. If AB = 5 cm, BC = 13 cm and AC = 12 cm, Find the area of ΔABC. Also find the length of AD.

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ABC is a triangle in. which ∠A=90∘,AN⊥BC,BC=12cm and AC = 5 cm. Find the ratio of the areas of ΔANC and ΔABC

In ΔANC and ΔABC ∠C = ∠C [Common] ∠ANC = ∠BAC [Each 90°] Then, ΔANC ~ ΔBAC [By AA similarity] By area of similarity triangle theorem

ABC is a triangle in. which $∠ A = 90^{\circ}, A N ⊥ B C, B C = 12 c m$ and AC = 5 cm. Find the ratio of the areas of $Δ A N C$ and $Δ A B C$