Home
Class 12
MATHS
One angle of an isosceles triangle is 12...

One angle of an isosceles triangle is `120^0` and the radius of its incricel is `sqrt(3)dot` Then the area of the triangle in sq. units is `7+12sqrt(3)` (b) `12-7sqrt(3)` `12+7sqrt(3)` (d) `4pi`

A

`4sqrt(3)`

B

`12-7sqrt(3)`

C

`12+7sqrt(3)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let `AB=AC=a and angleA=120^(@)`
`:.` Area of triangle `=(1)/(2)a^(2)sin120^(@)`
where `a=AD+BD=sqrt(3)tan30^(@)+sqrt(3)cot 15^(@)`
`=1+(sqrt(3))/(tan(45^(@)-15^(@))`

`rArra=1+sqrt(3)((1+tan45^(@)tan30^(@))/(tan45^(@)-tan30^(@)))`
`=1+sqrt(3)((sqrt(3)+1)/(sqrt(3)-1))=4+2sqrt(3)`
`:.` Area of a triangle
`=(1)/(2)(4+2sqrt(3))^(2)((sqrt(3))/(2))=(12+7sqrt(3))` sq units
Promotional Banner

Similar Questions

Explore conceptually related problems

One angle of an isosceles triangle is 120^0 and the radius of its incircle is sqrt(3)dot Then the area of the triangle in sq. units is (a) 7+12sqrt(3) (b) 12-7sqrt(3) (c) 12+7sqrt(3) (d) 4pi

If the angles of a triangle are 30^0a n d45^0 and the included side is (sqrt(3)+1)c m then the area of the triangle is______.

Two medians drawn from the acute angles of a right angled triangle intersect at an angle pi/6. If the length of the hypotenuse of the triangle is 3 units, then the area of the triangle (in sq. units) is (a) sqrt3 (b) 3 (c) sqrt2 (d) 9

In an equilateral triangle, three coins of radii 1 unit each are kept so that they touch each other and also the sides of the triangle. The area of the triangle is (fig) 4:2sqrt(3) (b) 6+4sqrt(3) 12+(7sqrt(3))/4 (d) 3+(7sqrt(3))/4

One vertex of an equilateral triangle is (2,2) and its centroid is (-2/sqrt3,2/sqrt3) then length of its side is

Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) 1-sqrt(2/3) (B) sqrt(3/2) -1 (C) 1+sqrt(2/3) (D) sqrt(3/2)+1

The incentre of a triangle with vertices (7, 1),(-1, 5) and (3+2sqrt(3),3+4sqrt(3)) is

In triangle A B C , if angle c is 90 and the area of triangle is 30 sq.units,then minimum possible value of hypotenuse c is equal to (a) 30sqrt(2) (b) 60sqrt(2) (c) 120sqrt(2) (d) 2sqrt(30)

On the line segment joining (1, 0) and (3, 0) , an equilateral triangle is drawn having its vertex in the fourth quadrant. Then the radical center of the circles described on its sides. (a) (3,-1/(sqrt(3))) (b) (3,-sqrt(3)) (c) (2,-1/sqrt(3)) (d) (2,-sqrt(3))

Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is 6sqrt3r .