Question

triangle ABC,angle B=90 degree D is the midpoint, BD=4.6 find AC​

Answer 1

Answer:

AC = 9cm

Explanation:

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.

Answer 2

$\huge \color{purple}ANSWER :$

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.