If a,b,c are the lengths of the perpendiculars dropped from a point inside on an equilateral triangle of side "p” on its sides, then find a+b+c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C

Let assume the point be centroid of the triangle.
The perpedicular distance from centroid to side of an equilateral triangle = $\frac{\sqrt{3} p}{6}$
a+b+c = $\frac{\sqrt{3} p}{2}$

Suggest Corrections

Similar questions

Q. P is a point inside the triangle ABC from which the length of perpendiculars drawn of the sides of lengths a,b,c are respectively p,q and r. Determine the position of p if

\frac{a}{p} + \frac{b}{q} + \frac{c}{r}

is minimum.

In an equilateral triangle ABC; points P, Q and R are taken on the sides AB, BC and CA respectively such that AP= BQ = CR. Prove that triangle PQR is equilateral.

Q. A point

P

is inside an equilateral triangle. If the distances of

P

from the sides are

8, 10, 12

units, the lengths of a side of the triangle is?

Q. ABC is an equilateral triangle with side a. A point P is taken inside ABC. The sum of lengths of perpendicular from P to all the sides is

Q. A point

P

is inside an equilateral triangle.If the distances of

P

from the sides are

4, 5, 6

units, the length of the side of the triangle is

Join BYJU'S Learning Program

If a,b,c are the lengths of the perpendiculars dropped from a point inside on an equilateral triangle of side "p” on its sides, then find a+b+c

The correct option is C Let assume the point be centroid of the triangle. The perpedicular distance from centroid to side of an equilateral triangle = √3p6 a+b+c = √3p2

The correct option is C

Let assume the point be centroid of the triangle.
The perpedicular distance from centroid to side of an equilateral triangle = $\frac{\sqrt{3} p}{6}$
a+b+c = $\frac{\sqrt{3} p}{2}$