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ΔABC is right angled at A and AD ⊥ BC. If BC = 13 cm and AC = 5 cm,then the ratio of the areas of ΔABC and ΔADC is ____.

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Detailed Solution

ΔABC is right angled at A and AD ⊥ BC. If BC = 13 cm and AC = 5 cm,then the ratio of the areas of ΔABC and ΔADC is

16925

.
Given that,
ΔABC is right angled at A and AD ⊥ BC where BC = 13 cm and AC = 5 cm.

ΔABC is right angled at A and AD ⊥ BC. If BC = 13 cm and AC = 5 cm, find the ratio of the areas of ΔABC and ΔADC. - Sarthaks eConnect | Largest Online Education Community

Consider the triangles

Δ A B C

and

Δ A D C

.
The angle BAC and angle ADC are the right angles.
So,

∠ B A C = ∠ A D C

The angle C is a common angle of the triangles ABC and ADC.
So,

∠ A C B = ∠ A C D

By the AA similarity pattern, the triangle ABC and ADC are similar.
That means,
∆ABC~△ADC
The ratio of the area of the triangles is equal to the ratio of the square of corresponding sides of the triangle.
That is,

a r e a Δ A B C a r e a Δ A D C = B C 2 A C 2 ⇒ a r e a Δ A B C a r e a Δ A D C = 13252 ⇒ a r e a Δ A B C a r e a Δ A D C = 16925

The ratio of the areas of the triangle is

16925

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