Home
Class 12
MATHS
In a triangle ABC, it is known that AB=A...

In a triangle ABC, it is known that AB=AC. Suppose D is the mid-point of AC and BD=BC=2. Then the area of the triangle ABC is-

A

2

B

`2sqrt2`

C

`sqrt7`

D

`2sqrt7`

Text Solution

Verified by Experts

The correct Answer is:
C

We know
`AB^(2)+BC^(2)=2(CD^(2)+BD^(2))`
`AB^(2)+4=2((AB^(2))/(4)+4)`
`AB^(2)+4=(AB^(2))/(4)+8`
`(AB^(2))/(2)=4`
`AB^(2)=8`
`AB=2sqrt2`
Now
Area `=(1)/(2)xx2xxsqrt7=sqrt7`
Promotional Banner

Topper's Solved these Questions

  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART-2(MATHEMATICS)|10 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART -I MATHEMATICS|20 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART-I MATHEMATICS|15 Videos

  • KVPY 2021

    KVPY PREVIOUS YEAR|Exercise PART II MATHEMATICS|4 Videos

Similar Questions

Explore conceptually related problems

In ∆ABC, AD is the bisector of ∠A meeting BC at D, CF ⊥ AB and E is the mid-point of AC. Then median of the triangle is

In a Delta ABC, if D is the mid point of BC and AD is perpendicular to AC, then cos B=

let ABC be a triangle with AB=AC. If D is the mid-point of BC, E the foot of the perpendicular drawn from D to AC,F is the mid-point of DE.Prove that AF is perpendicular to BE.

In a triangle ABC, the angle bisector BD of angleB intersects AC in D. Suppose BC=2, CD=1 and BD=(3)/(sqrt(2)) . The perimeter of the triangle ABC is

In the given figure, in triangle ABC, D is the mid-point cf AB and P is any point on BC. If CQ || PD meets AB in Q and area of triangle ABC = 30 cm2, then, area of triangle BPQ is

In a Delta ABC , D is the mid point of side AC such that BD =1/2 AC . angleABC is ?.

In a triangle ABC, angleB=90^(@), D is the midpoint of AC, BD=sqrt117 . Sum of sides of AB & BC is 30 cm. Find the area of triangle ABC.