Question

The sides of a triangle are x, x+1, 2x-1. It's area is x• 10 sq. units. Find the value of x
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Answer 1

Step-by-step explanation:

GIVEN THAT:

|AB|=x

|BC|=x+1

|AC|=2x-1

AREA IF TRIANGLE: 10x sq.units

First we have to find the coordinates of vertexes of triangle. Let's suppose the vertexes of triangle be "A", "B" and "C"

In order to find the coordinates of the vertex we have to solve the equations of those sides which are intersecting at that vertex.

FOR THE COORDINATES OF A;

|AB|=x

|AC|=2x-1

Add both the equations. We get 3x-1.

3x-1=0

3x=1

x=1/3. coordinates of A are (1/3,0)

FOR THE COORDINATES OF B;

|AB|=x

|BC|=x+1

By adding both equations we get 2x+1

2x-1=0

2x=1

x=1/2. coordinates of B are (1/2,0)

FOR THE COORDINATES OF C;

|AC|=2x-1

|BC|=x+1

By adding both equations we get 3x

3x=0

x=0 coordinates of C are (0,0)

FORMULA TO FIND AREA OF TRIANGLE:

AREA=

$1 \div 2 |x1 \: \: \: \: y1 \: \: \: \: \: 1 | \ \\ |x2 \: \: \: y2 \: \: \: 1 | \\ |x3 \: \: \: y3 \: \: \: 1 |$

Considering Coordinates of A,B and C as (x1,y1)

, (x2,y2) and (x3,y3) respectively.

Now putting the values in formula..

10x= 1/2 |1/3. 0. 1|

|1/2. 0. 1|

|0. . 0. 1|

10x = 1/2. { 1/3(0-0) - 0(1/2-0) + 1(0-0)}

10x = 1/2 { 0-0+0}

10x = 0

The value of x is 0.