Question

triangle ABC is isosceles in which AE is perpendicular BC, AE = 6cm, BC =9cm, the area of triangle ABC is ​

Answer 1

Given, △ABC, AB=AC, BC=9

Perpendicular from A on BC meets at E, let AE=p=6

Area of △ABC =

2

1

×base×height=

2

1

×p×9 =

2

1

(6)(9)=27

As △ABC is an Isosceles triangle, the perpendicular divides the base in two equal halves:

In △AEB

AE

2

+BE

2

=AB

2

AB=

6

2

+(

2

9

)

2

=

36+

4

81

cm =

4

144+81

=

2

15

cm

Now, Area(ΔABC)=

2

1

×AB×CD

⇒27=

2

1

×

2

15

×CD

⇒CD=7.2.....

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