math
posted by avadhesh .
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

let AD = DC = x
then AB = 2x
in triangle ABC , angle B = angle C =Ø
in triangle BCD , angle C = angle BDC = Ø
2 angles of one are equal to 2 angles of the other, so they are similar
then:
2/x = 2x/2
2x^2 = 4
x^2=2
x=√2
So triangle ABC has equal sides of 2√2 and a base of 2
which is similar to
√2 : √2 : 1
Using the cosine law we can find angle A
1^2 = √2^2 + √2^2  2(√2)(√2)cosA
4cosA = 3
cosA = 3/4
then sinA = √7/4
area ABC = (1/2)(2e√2)(2√2)(√7/4)= √7
check my arithmetic, should have written it out first.
Respond to this Question
Similar Questions

Geometry
D is the midpoint of side AB of the triangle ABC, E is midpoint of CD and F is midpoint of AE. Prove that: Area (triangle AFD) =Area (triangle ABC). 
mathsareas
in triangle ABC P, Q AND R ARE the mid points of side AB, BC, CA.prove that area of parallelogram APQR=( 1/2)* area of triangle[ABC] 
geometry
Open that link please please help me with my assignments 1. in the figure , the areas of traingle cef, triangle abe, triangle adf are 3,4, and 5 respectively. find the area of triangle aef 2. equialateral triangle abc has an area of … 
Geometry
Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC. a) Draw a triangle ABC and then sketch the remainder of the figure. It will help if (triangle) … 
sanket study centre
In triangle ABC p,q,r such that they lie interior of triang ABC and AP=AR and all the three sides of triangle PQR are scalan if area of triangle PQR is 100 then find area of triangle ABC 
mats
AD is the mid point of triangle ABC and G divides AD in the ratio 2:1 .Prove that triangle AGB =area BGC = area AGC =1Ã·3 area ABC 
maths
DRAW LOCUS OF POINT SO THAT IT IS EQUIDISTANT FROM BC & CA . ... constructed such that none of these triangles overlaps triangle ABC. a) Draw a triangle ABC and then sketch ... 16) AB = 3.2cm BC = 8.4cm The area of the triangle ABC … 
math
In isosceles right triangle ABC, point D is on hypotenuse BC such that AD is an altitude of triangle ABC and DC = 5. What is the area of triangle ABC? 
Maths
In triangle ABC ,D and E are the mid points of BC and AC respectively prove that the area of triangle ABC is 4 times than triangle ABE 
maths
In a triangle ABC,D and E are the mid points of BC and AD respectively.prove that the area of triangle ABC is four times to the area of triangle ABE