Question

4. From a point in the interior of an equilateral
triangle, perpendiculars are drawn on the
three sides. The lengths of the perpendiculars
are 8 cm, 10 cm and 11 cm. Find the area of
the triangle correct to two decimal places.
Take V3 =1.73.​

Answer 1

Answer:

For an equilateral triangle of side a cm , the area is 12a×a×sin60∘=3√4a2 cm2 .

This triangle is divided into three triangles each with a base length of a and perpendicular heights of 8,10 and 11 cm respectively. So the total area is 12×a×8+12×a×10+12×a×11=14.5a cm2 .

So 3√4a2=14.5a

3√4a=14.5

a=583√ cm

Therefore, the area is 14.5×583√=485.55 cm2 .

Check: 3√4×(583√)2=485.55 cm.