Home
Class 12
MATHS
Let ABC be an equilateral triangle, le...

Let ABC be an equilateral triangle, let KLMN be a rectangle with K, L on BC , M on AC and N on AB. Suppose `AN//NB = 2` and the area of triangle BKN is 6. The area of the triangle ABC is -

A

54

B

108

C

48

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B

`y=(sqrt(3)x)/(2),z=(x)/(2)`
Area of `Delta BKN` is 6
`therefore (1)/(2)yz=6 rArr x^(2)=(48)/(sqrt(3))`
Area of `Delta ABC = 6+6+2xy +(1)/(2)(2x)(2x)sin 60^(@)`
`=12+2x(sqrt(3)x)/(2)+2x^(2)(sqrt(3))/(2)`
`=12+2sqrt(3)xx(48)/(sqrt(3)=108`
Promotional Banner

Topper's Solved these Questions

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|13 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE PUBLICATION|Exercise Archives|1 Videos

  • STATISTICS

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

An equilateral triangle of side 6 cm. Its area is :

If Delta ABC be an equilateral triangle and AD _|_BC , then AD^(2) =

ABC is an equilateral triangle. D and E are the mid-points of AB and AC. Then angleADE=

Let A B C be a triangle with /_B=90^0 . Let AD be the bisector of /_A with D on BC. Suppose AC=6cm and the area of the triangle ADC is 10c m^2dot Find the length of BD.

In a triangle ABC if sinAsinB=(ab)/(c^(2)) , then the triangles is

In a triangle ABC, if a =2x, b=2y and C=120^(@), then the area of the triangle is-

(iv) The centroid of the Delta ABC is G, If the area of the Delta GBC be 12 Sq. cm, the area of the Delta ABC is

(vi) Delta ABC is an equilateral triangle of sides 6 cm. If G be its centroid, find the length of AG.

In a triangle ABC, if (cos A)/(a) =(cos B)/(b ) =(cos C)/(c) and the side a=2, then the area of the triangle is-

Let ABC be a triangle of area 24sq.units and PQR be the triangle formed by the mid-points of the sides triangle ABC. Then what is the area of triangle PQR.