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|Exercise Multiple Correct Answers Type|13 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE|Exercise Comprehension Type|6 Videos

  • SETS AND RELATIONS

    CENGAGE|Exercise Question Bank|15 Videos

  • STATISTICS

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

Let ABC be a triangle with angleB=90^(@) . Let AD be the bisector of angleA with D on BC. Supose AC = 6 cm and the area of the triangle ADC is 10 cm^(2) . Then the length of BD in cm is equal to

angle ACB is an angle in the semicircle of diameter AB = 5 and AC : BC = 3:4. The area of the triangle ABC is

angle ACB is an angle in the semicircle of diameter AB =5 and AC : BC = 3 : 4 The area of the triangle ABC is

Let ABC be a triangle with /_B=90^(@). Let AD be the bisector of /_A with D on BC . Suppose AC=6cm and the area of the triangle ADC is 10cm^(2). Find the length of BD.

In a triangle ABC,having AD is median and area of triangle ABD=120m^(2). Find area of triangle ABC.