∆ABC is right angled at A and AD⊥BC. If BC = 13cm and AC = 5cm, find the ratio of the areas of ∆ABC and ∆ADC.

Home » ∆ABC is right angled at A and AD⊥BC. If BC = 13cm and AC = 5cm, find the ratio of the areas of ∆ABC and ∆ADC.

∆ABC is right angled at A and AD⊥BC. If BC = 13cm and AC = 5cm, find the ratio of the areas of ∆ABC and ∆ADC.

Answer:

In ∆ABC and ∆ADC,

∠???????????? = ∠???????????? = 900

∠???????????? = ∠???????????? (????????????????????????)

By AA similarity,

∆ BAC~ ∆ ADC.

The ratio of the areas of these triangles is equal to the ratio of squares of their corresponding sides.

$\frac{a r(\triangle B A C)}{\operatorname{ar}(\triangle A D C)}=\frac{B C^{2}}{A C^{2}}$

$\frac{\operatorname{ar}(\triangle B A C)}{a r(\triangle A B C)}=\frac{13^{2}}{5^{2}}$

$\frac{\operatorname{ar}(\triangle B A C)}{\operatorname{ar}(\Delta A B C)}=\frac{169}{25}$

The ratio of areas of both the triangles is 169:25

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