Question

in the following figure angle abc = 90 degree and BD is perpendicular to AC if ab = 8 cm CD = 2 cm find the length of BD​

Answer 1

Answer:

In Right Δ ABC and Right Δ C DB

∠ABC=∠C DB=90°

∠ C is common.

Δ ABC ~ Δ C DB→→[ AA similarity criterion]

When triangles are similar , their corresponding sides are proportional.

$\frac{AB}{CD}=\frac{BC}{BD}\\\\ \frac{8}{2}=\frac{BC}{BD}\\\\ BC= 4*BD$

In Right Δ B D C

By Pythagoras theorem

BC²= B D²+DC²

(4* BD)²= BD²+2²

16 BD²- BD²=4

15 * BD²=4

$BD^2=\frac{4}{15}\\\\ BD=\frac{2}{\sqrt{15}}$

BD=0.516 cm(approx.)