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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. BD = ___ cm if AD = DC = 5 cm.

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Solution

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

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

Since △ ABC is right angled triangle 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. BD = ___ cm if AD = DC = 5 cm.

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