Math, asked by arshpreets313, 2 months ago

(iv) If BD = 6 m, DC = 9 m and ar (A ABC) = 56 sq m, then the length of sides AB and AC are respectively.​

Answers

Answered by kruthikashetty016
2

Step-by-step explanation:

In the given figure, ΔABC circumscribed the circle with centre O.

Radius OD=3cm

BD=6cm,DC=9cm

Area of ΔABC=54cm

2

To find : Length of AB and AC.

AF and EA are tangents to the circle at point A.

Let AF=EA=x

BD and BF are tangents to the circle at point B.

BD=BF=6cm

CD and CE are tangents to the circle at point C.

CD=CE=9cm

Now, new sides of the triangle are:

AB=AF+FB=x+6cm

AC=AE+EC=x+9cm

BC=BD+DC=6+9=15cm

Now, using Heron's formula:

Area of triangle ABC=

s(s−a)(s−b)(s−c)

Where S=

2

a+b+c

S=1/2(x+6+x+9+15)=x+15

Area of ABC=

(x+15)(x+15−(x+6))(x+15−(x−9))(x+15−15)

Or

54=

(x+15)(9)(6)(x)

Squaring both sides, we have

54

2

=54x(x+15)

x

2

+15x−54=0

Solve this quadratic equation and find the value of x.

x

2

+18x−3x−54=0

x(x+18)−3(x+18)=0

(x−3)(x+18)=0

Either x=3 or x=−18

But x cannot be negative.

So, x=3

Answer :-

AB=x+6=3+6=9cm

AC=x+9=3+9=12cm

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