Math, asked by chandanarajput, 11 months ago

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​

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Answered by CarlynBronk
3

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.)

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