Question

From a point within an equilateral are drawn to the three sides are 4 , 7 , 9 respectively . Find the the area of triangle​

Answer 1

Answer:

A point inside an equilateral triangle is 3 cm, 4 cm and 5cm respectively from each of its sides.What is the area of the triangle?

Let △ ABC be the equilateral triangle, and the point P in it is such that the perpendicular distances from the sides BC, AB and AC are PD=3 cm, PE=4 cm and PF=5 cm respectively.

Let the length of each side of the equilateral triangle be L cm.

Now we have,

ΔABC=ΔPBC+ΔPAB+ΔPAC

=12PD.AC+12PE.AB+12PF.AC

=L2(PD+PE+PF)

=L2(3+4+5)=6L cm2.

Now, since ΔABC is an equilateral triangle with side L , its area is given by the formula 3√4L2 .

So 3√4L2=6L .

⟹L=83–√

Hence the area of the given equilateral triangle is 48 3–√ cm2 .

Hope it helps

Step-by-step explanation:

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Answer 2

Answer:

3√4L2=6L

= L =83-√

The area of the given equilateral triangle is 48 3 - √ cm2.

Hope it will help you