Question

In the given figure, BD 1 AC and CE I AB. If BD=CE=3.5 cm and AB = 5 cm, then the measure of AC is (a) 3.5 cm ) (b) 4.5 cm (c) 5 cm .​

Answer 1

Solution :-

given that,

→ BD ⟂ AC .

→ CE ⟂ AB .

→ BD = CE = 3.5 cm

→ AB = 5 cm .

So, in ∆ADB and ∆AEC we have,

→ ∠ADB = ∠AEC { Each 90° }

→ ∠DAB = ∠EAC { common }

→ BD = CE { given }

then,

→ ∆ADB ~ ∆AEC { By AAS congruence rule }

therefore,

→ AB = AC { By CPCT }

hence,

→ AC = 5 cm (c) (Ans.)

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