Question

For what values of x and y must the figure have in order to be a parallelogram

Answer 1

Given:

Given that the parallelogram with the lengths 5x, 3x + 1, 2y - 5 and y.

We need to determine the values of x and y.

Values of x and y:

We know the property that the opposite sides of a parallelogram are congruent.

Thus, we have;

`5x=2y-5` ------- (1)

`3x+1=y` ------- (2)

The value of x and y can be determined using the substitution method.

Substituting equation (2) in equation (1), we have;

`5x=2(3x+1)-5`

`5x=6x+2-5`

`5x=6x-3`

`-x=-3`

`x=3`

Thus, the value of x is 3.

Substituting x = 3 in equation (2), we have;

`3(3)+1=y`

`9+1=y`

`10=y`

Thus, the value of y is 10.