Question

In triangle $ABC$ measure is $\angle B=90$ and $BM$ is an altitude if $AM=BM=8$.Then find AC

• A. 16
• B. 18
• C. 12
• D. 20

Answer 1

The correct option is A 16

We have,

$BM$ is an altitude of $\Delta ABC$

Given $\Delta ABC={90}^o$

Also given that,

$AM=BM=8$

We know that,

According to given question,

$\Delta ABC\sim \Delta AMB$

Then,

$\frac{AB}{AM}=\frac{BC}{BM}$

$\Rightarrow \frac{AB}{8}=\frac{BC}{8}$

$\Rightarrow AB=BC......\left(1\right)$

$In\Delta ABM,\angle AMB={90}^o$

By Pythagoras theorem,

$A{B}^2=A{M}^2+B{M}^2$

$A{B}^2=x^2+x^2$

$A{B}^2=2x^2$

by equation (1) to and we get,

$AB=BC$

$A{B}^2=B{C}^2=2x^2$

Then,

$In\Delta ABC$

$A{C}^2=A{B}^2+B{C}^2$

$\Rightarrow 2x^2+2x^2=A{C}^2$

$\Rightarrow A{C}^2=4x^2$

$\Rightarrow AC=2x$

$\Rightarrow AC=2\times 8$

$\Rightarrow AC=16$.

Hence, this is the answer.