Question

State whether the following statement is true or false.

M∠B=90 in ΔABC. BM is altitude to AC. If AM=BM=8, then AC=16.

• A. True
• B. False

Answer 1

The correct option is A True

In ∆ABC , $\angle B=90°$

BM is an altitude of AC.

AM = BM = 8

In ∆ABC and ∆AMB ,

$\angle$A = $\angle$A ( common angle )

$\angle$ABC = $\angle$AMB = 90°

∆ABC ~ ∆AMB ( By A.A similarity )--( 1 )

Similarly ∆ABC ~ ∆BMC ------( 2 )

From ( 1 ) and ( 2 ), we get,

∆AMB ~ ∆BMC

AM/BM = BM/MC

[ If two triangles are similar then corresponding sides are proportional )

BM² = MC × AM

8² = MC × 8

MC = 8²/8

MC = 8

AC = AM + MC

= 8 + 8

AC = 16.