Question

please answer this question ​

Answer 1

Answer:

169 : 25

Step-by-step explanation:

In ΔABC and ΔADC,

∠C = ∠C  (Common)

∠BAC = ∠DAC  (90° each)

∴ ΔACB ~ ΔACD  (AA Similarity)

$\frac{BC}{CA}$ = $\frac{CA}{AD}$  and   $\frac{AB}{DC}$ = $\frac{AC}{AD}$  (proportional sides)    → (1)

[BC = 13 cm, AC = 5 cm, AB = 12 cm( pythagoras theorem)]

from (1) we get,

AD = $\frac{25}{13}$  and DC = $\frac{60}{13}$  

Now,

area(ΔABC) = $\frac{1}{2}$  × AB ×AC   and   area(ΔADC) =

taking their ratios,

$\frac{area(ABC)}{area(ADC)}$ = $\frac{AB*AC}{DC*AD}$ = $\frac{169}{25}$

∴ The ratio of their areas are 169 : 25.

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