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Mathematics

Perpendicular from Right Angle to Hypotenuse Divides the Triangle into Two Similar Triangles

ABC is right ...

Question

$△$ ABC is right angled at B and the perpendicular drawn to the opposite side bisects it at D. if $A D = D C = 5 c m, B D =$ ___ $c m$

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Solution

Since, $△$ ABC is right angled at B and BD is the perpendicular drawn to the opposite side,
${B D}^{2} = A D \times D C$
$\Rightarrow {B D}^{2} = 5 \times 5$
$\Rightarrow B D = \sqrt{25} = 5 c m$

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△ ABC is right angled at B and the perpendicular drawn to the opposite side bisects it at D. if AD=DC=5 cm, BD= ___ cm

Since, △ ABC is right angled at B and BD is the perpendicular drawn to the opposite side, BD2=AD×DC ⇒BD2=5×5 ⇒BD=√25=5 cm

$△$ ABC is right angled at B and the perpendicular drawn to the opposite side bisects it at D. if $A D = D C = 5 c m, B D =$ ___ $c m$

Since, $△$ ABC is right angled at B and BD is the perpendicular drawn to the opposite side,
${B D}^{2} = A D \times D C$
$\Rightarrow {B D}^{2} = 5 \times 5$
$\Rightarrow B D = \sqrt{25} = 5 c m$