Question

solve the problem . answer is 24m,4.8cm

Answer 1

Given:

ABC is a right angle triangle right angled at A.
AB=8 cm.
BC=10 cm.
AC=6 cm.
AD is the perpendicular.

Find:

1. AD.
2. Area of ABC.


Answer :

AD divides ABC into 2 right angle triangles , ABD and ACD.

AD is the common side for both the triangles.

According to Pythagorean theorem :

a²+b²=c².

In both the triangles we only know the measurement of their hypotenuse .

In ABD:

AD²=AB²-BD².

AD²=8²-BD².

AD²=64-BD²— Equation 1.

In ACD:

AD²=AC²-DC².

AD²=6²-DC².

AD²=36-DC² —Equation 2.

We can see that, the LHS of both the equations is the same.

So, according to Euclid's axiom : Things which are equal to the same thing are equal to one another;

64-BD²=36-DC².

Grouping like terms on the same side:

64-36=BD²-DC².
28=BD²-DC².

Identity to be used: a²-b²=(a+b)(a-b).

28=(BD+DC)(BD-DC)

BD+DC=BC=10 cm.

28=10(BD-DC).
28/10=BD-DC.
2.8=BD-DC.

Adding (BD+DC) and (BD-DC)

BD+DC=10.
BD-DC=2.8.

2BD=12.8

BD=12.8/2.
BD=6.4.

Therefore,

64-6.4²=AD².
64-40.96=AD².
23.04=AD².
√23.04=AD.
4.8=AD.

AD = 4.8 cm.

2. Area of ABC = 1/2*BC*AD.

=1/2*10*4.8.
=48/2.
=24 cm².