Question

In a ∆ ABC,DE || BC. If AD = 1.75 cm, AB = 7 cm and AE = 2 cm, then find AC.​

Answer 1

Step-by-step explanation:

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Answer 2

The answer is 8cm

GIVEN

In a ∆ ABC,DE || BC. If AD = 1.75 cm, AB = 7 cm and AE = 2 cm.

TO FIND

AC

SOLUTION

We can simply solve the above problem as follows;

In ΔABC and ΔADE

∠A = ∠A (Common angle)

∠ABC = ∠ADC (Alternate angles are equal)

∠ACB = ∠AED (Alternate angles are equal)

By A-A-A similarity criterion

ΔABC ≈ ΔADE

Sides of similar triangles are proportional to each other.

Therefore,

$\frac{AB }{AD} = \frac{AC}{AE}$

Putting the values in the above formula we get;

$\frac{7}{1.75} = \frac{AC}{2}$

Cross multiplying

7×2 = 1.75 × AC

AC = 14/1.75 = 8cm

Hence, The answer is 8cm

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