Question

In ΔABC, AP ⊥ BC, BQ ⊥ AC. If AP = 7, BQ = 8 and BC = 12, then find AC.

Answer 1

Given: AP ⊥ BC, BQ ⊥ AC

Now, in ΔAPC and ΔBQC

∠APC ≅ ∠BQC  ......[Each equal to 90°]

∠ACP ≅ ∠BCQ  .....[Common angle]

∴ By AA criterion of similarity,

ΔAPC ∼ ΔBQC

So, `(AP)/(AC) = (BQ)/(BC)`  ......[C.S.S.T.]

Here, AP = 7, BQ = 8, BC = 12

Substituting the values,

`7/(AC) = 8/12`

⇒ AC × 8 = 7 × 12

⇒ AC = `(7 xx 12)/8` = 10.5

Hence, the value of AC is 10.5.