Question

$△$ ABC a right-angled triangle, find the length of BD assuming $△ABC\sim △BDC$

• A. 8.6 units
• B. 9.6 units
• C. 6 units
• D. 10 units

Answer 1

The correct option is B

9.6 units

Given :$△ABC\sim △BDC$

The ratio of corresponding sides of similar triangles are equal. Hence,

$\frac{AB}{BD}=\frac{AC}{BC}$

i.e.,$\frac{12}{BD}=\frac{AC}{16}$

Using Pythagoras theorem,

we have$AC=\sqrt{B{C}^2+A{B}^2}$ = $\sqrt{{16}^2+{12}^2}=\sqrt{400}=20$ units

Now, $\frac{12}{BD}=\frac{20}{16}$

$⟹BD=\frac{12\times 16}{20}$

$⟹BD=9.6$ units