Question

in the given figure DE is parallel to bc. if ad = 2.5 cm, bd = 3cm and ae = 3.5 . find the length of ac​

Answer 1

Given:

DE is parallel to BC

AD = 2.5 cm

BD = 3cm

AE = 3.5

To find:

The length of AC

Solution:

In ΔADE & ΔABC since DE // BC, we have

∠ADE = ∠ABC ...... [corresponding angles]

∠AED = ∠ACB ...... [corresponding angles]

∠DAE = ∠BAC ...... [common angle]

∴  ΔADE ~ ΔABC ...... [By AAA Similarity]

We know that → the corresponding sides of the two similar triangles are proportional to each other.

∵ ΔADE ~ ΔABC

∴ $\frac{AD}{AB} = \frac{AE}{AC}$

$\implies \frac{AD}{AD + BD} = \frac{AE}{AC}$

substituting the values of AD, BD & AE

$\implies \frac{2.5}{2.5 + 3} = \frac{3.5}{AC}$

$\implies \frac{2.5}{5.5} = \frac{3.5}{AC}$

$\implies AC= \frac{3.5\times 5.5}{2.5}$

$\implies AC= \frac{19.25}{2.5}$

$\implies \bold{AC= 7.7\:cm}$

Thus, the length of AC is → 7.7 cm.

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