Question

In ABC ,D is the midpoint of hypotenues AC. If BD=4.5,then AC=?
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Answer 1

Step-by-step explanation:

In triangle ABC, angle B=90 degrees. D is the midpoint of side AC and BD=4.5cm. What is the length of side AC?

Flexible support where it's needed.

GIVEN: A right triangle ABC. D bisects AC. AD= DC & BD = 4.5cm

TO FIND: the length of AC.

CONSTRUCTION: Extend BD up to P, such that BD = DP = 4.5cm. Join AP & CP.

Since in quadrilateral ABCP, diagonals bisect each other. So, ABCP is a parallelogram.

But angle B = 90°

So, parallelogram ABCP should be a rectangle.

Therefore, diagonals AC = BP ( diagonals of a rectangle are equal)

But BP = 4.5+4.5 = 9cm

So, AC = 9cm.