Maths-

General

Easy

Question

Hint:

**Hint :-** let the side of equilateral triangle be x , then we get height of equilateral triangle as .Now , Find length of DE and apply pythagoras theorem in Right angle triangle ADE to find length of AD in terms of AB.

## The correct answer is: Hence proved

### Aim :- Prove that

Explanation(proof ) :-

BK:KC = 2:1 KC :( KC+BK) = 1:(1+2) KC :CB = 1:3

In equilateral triangle all sides are equal

Let , AB = BC = CA = x

Given CK = BC = ( BC is trisected at K)

In equilateral triangle ,the altitudes and medians coincide

so,AE is median also i.e E is midpoint of BC

CE =

From diagram ,KE = CE - CK =

We get height of equilateral triangle when side x is

Applying pythagoras theorem on triangle ADE

We get,

Substitute x by AC as x = AC

Hence proved

### Related Questions to study

Maths-

### The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that

### The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that

Maths-General

Maths-

### In an equilateral the side BC is trisected at D . Prove that

.

### In an equilateral the side BC is trisected at D . Prove that

.

Maths-General

Maths-

ABC and DBC are two isosceles triangles on the same base BC. Show

that

ABC and DBC are two isosceles triangles on the same base BC. Show

that

Maths-General

Maths-

### PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R

### PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R

Maths-General

Maths-

### Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5

### Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5

Maths-General

Maths-

### In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.

### In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.

Maths-General

Maths-

Maths-General

Maths-

### Classify whether the following Surd is rational or irrational , justify 4√5+ 9

### Classify whether the following Surd is rational or irrational , justify 4√5+ 9

Maths-General

Maths-

### PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.

### PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.

Maths-General

Maths-

Maths-General

Maths-

### Classify whether the following Surd is rational or irrational , justify 8-√48

### Classify whether the following Surd is rational or irrational , justify 8-√48

Maths-General

Maths-

### Classify whether the following Surd is rational or irrational , Justify.√47+√8

### Classify whether the following Surd is rational or irrational , Justify.√47+√8

Maths-General

Maths-

### In the figure, sides QP and RQ of a are produced to points S and T respectively.

If and, find.

### In the figure, sides QP and RQ of a are produced to points S and T respectively.

If and, find.

Maths-General

Maths-

### Simplify √8 - √18 + √50

### Simplify √8 - √18 + √50

Maths-General

Maths-

Maths-General