Question

A triangle is right angled at b and e are points on bc trisect it,if ab=8cm,bc=6cm then
a)ae^2=80
b)AC^2=100
c)AD^2=68
d)8AE^2=3AC^2-5AD^2
Answer it in srep by step explanation

Answer 1

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MATHS

In right angled Triangle ABC if D and E trisect BC then prove that 8AE

2

=3AC

2

+5AD

2

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ANSWER

Since D and E are the points of trisection of BC therefore BD=DE=CE

Let BD=DE=CE=x.

Then BE=2x and BC=3x

In rt △ABD,

AD

2

=AB

2

+BD

2

=AB

2

+x

2

(i)

In rt △ABE,

AE

2

=AB

2

+BE

2

=AB

2

+4x

2

(ii)

In rt △ABC,

AC

2

=AB

2

+BC

2

=AB

2

+9x

2

(iii)

Now, 8AE

2

−3AC

2

−5AD

2

=8(AB

2

+4x

2

)−3(AB

2

+9x

2

)−5(AB

2

+x

2

)

=0

Therefore, 8AE

2

=3AC

2

+5AD

2