Question

(c) The measures of the sides of a triangle are ( 5/3x+y+1/2) cm, (2x +1/2 y) cm and (2/3x + 2y + 5/2) cm For what values of x and y is the triangle equilateral? Also, find the measure of a side of the triangle​

Answer 1

Answer:

The given triangle is equilateral then,

2x+

2

y

=

3

5x

+y+

2

1

⇒2x+

2

y

−

3

5x

−y=

2

1

⇒

3

x

−

2

y

=

2

1

⇒

6

2x−3y

=

2

1

⇒2x−3y=3(1)

3

5x

+y+

2

1

=

3

2x

+2y+

2

5

⇒

3

5x

−

3

2x

+y−2y=

2

5

−

2

1

⇒x−y=2(2)

Multiply (2) by 2 , 2x−2y=4(3)

Subtract (3) from (1), we get

2x−3y=3

−2x+2y=−4

−y=−1⇒y=1

From (2) , x−1=2⇒x=3

∴a=2x+

2

y

=2×3+

2

1

=

2

13

b=

3

5x

+y+

2

1

=5+1+

2

1

=

2

10+2+1

=

2

13

c=

3

2x

+2y+

2

5

=2+2+

2

5

=

2

4+4+5

=

2

13

Perimeter =3×

2

13

=

2

39