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In the picture, the perpendicular is drawn from the midpoint of the hypotenuse of a right triangle to the base. Calculate the length of the third side of the large right triangle and the lengths of all three sides of small right triangle.

1 Answer

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Best answer

AC = 10 cm

∴ AM = 5 cm

MN, CB are perpendicular to AB

MN, CB are parallel lines.

∴ MN divides AB and AC in the same ratio.

∴ AN = BN = 4cm

BC = \(\sqrt{10^2-8^2}=\sqrt{100-64}=\sqrt{36}\) = 6 cm

M is the midpoint of the AC. N is the midpoint of AB.

The length of the line joining the midpoints of two sides of a triangle is half the length of the third side. So MN is half of BC.

∴ MN = 3cm

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