Question

Two mutually perpendicular straight lines through the origin froam an isosceles triangle with the line 2x+y=5 .then the area of tge triangle is

Answer 1

Answer

Area of isosceles  triangle  = 12.5 unit square

Explanation

From the figure associated with this answer shows that, two mutually perpendicular straight lines through the origin from an isosceles triangle ABC  with the line BC is  2x+y=5 .

In triangle ABC, x coordinate of A and C is 0 and y coordinate of B is zero

AB= BC and  AO = CO

Find  Coordinate of A and C

y= 0, equation becomes,  2x = 5

x= 5/2

Coordinate of A(-5/2,0) and coordinate of C(5/2, 0)

Find  Coordinate of B

Here x=0, equation becomes, y = 5

we get B(0,5)

Find AC and BO

Let A(-5/2,0) and C(5/2, 0) then AC = 5

Let B(0,5) and O(0,0) then BO = 5

Find the area of triangle ABC

Area ,  A = 1/2 x AC x BO

          A =  1/2 x 5 x 5 = 25/2 = 12.5 unit square

Answer 2

Given:

Isosceles triangle,

Line = 2x + y = 5

To find:

The area of the triangle.

Solution:

Solve for x,

Put y= 0,

2x = 5

x = 5/2

As it passes through the origin,

x is the coordinate of A and C

A ( -5/2, 0 )

C ( 5/2 ,0 )

Solve for y,

Put x=0,

y = 5

Hence,

B ( 0, 5 )

To find the length of AC,

By formula,

Distance = √ ( y2 - y1 )^2 + ( x2 - x1 )^2

Here,

x1 = -5/2

y1 = 0

x2 = 5/2

y2 = 0

Substituting,

We get,

The length of AC = 5

To find the length of BO,

Where O is the origin.

Here,

x1 = 0

y1 = 5

x2 = 0

y2 = 0

Hence, The length of BO = 5

The area of the triangle,

Area = 1/2 * Base * Height

Here,

Base = AC = 5

Height = BO = 5

Substituting,

Area =  1/2 * 5 * 5

12.5 sq.units

Hence, The area of the triangle is 12.5 sq.units