Question

Find BD=______ cm ...​

Answer 1

By Pythagoras Therom

In △ABC

(AC) ² = (AB) ² + (BC) ²

(AC) ² = (30) ² + (40) ²

(AC) ² = 900 + 1600

(AC) ² = 2500

(AC) = √2500

AC = 50 cm

AC = 2DC (The altitude of a right triangle divides the right-angled triangle into two similar triangles.)

AD + DC = AC

2DC = AC

AC/2 =DC

DC = 50/2

DC = 25 cm

By Pythagoras Therom

In△BCD

(BC)² = (CD)² + (BD)²

(40)² = (25)² + (BD)²

1600 = 625 + (BD)²

(BD)² = 1600 - 625

(BD) = √975

BD = 31.224989992

Answer 2

Step-by-step explanation:

ΔABC is a right angle triangle:

AC is hypotheneus

30^2+40^2 = 2500

$\sqrt\62500$ = 50cm =AC

Let AD = DC

AD + DC = AC

AD +AD = 50cm

2AD = 50cm

AD = 25cm

ΔADB is a right angle triangle:

AB is hypotheneus

30^2 - 25^2 = 900 - 625 = 275cm

√257cm = BD

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