Question

Find the value of each variable in the variable in the following parallelograms

Answer 1

Given:

JKML is a parallelogram.

`JK=7x+10,KL=5y+14,ML=9x-12,\text{ and }JM=104.`

Required:

We need to find the value of x and y,

Step-by-step explanation:

We know that the opposite sides of the parallelogram are equal.

JK and ML are opposite sides of the given parallelogram.

`JK=ML`

`Substitute\text{ }JK=7x+10and\text{ }ML=9x-12\text{ in the equation.}`
`7x+10=9x-12`

Add 12 to both sides of the equation.

`7x+10+12=9x-12+12`

`7x+22=9x`

Subtract 7x from both sides of the equation.

`7x+22-7x=9x-7x`

`22=2x`

Divide both sides of the equation by 2.

`(22)/(2)=(2x)/(2)`
`11=x`

We get x=11.

KL and JM are opposite sides of the given parallelogram.

`KL=JM`

`Substitute\text{ }KL=5y+14\text{ and }JM=104\text{ in the equation.}`

`5y+14=104.`

Subtract 14 from both sides of the equation.

`5y+14-14=104-14`

`5y=90`

Divide both sides of the equation by 5.

`(5y)/(5)=(90)/(5)`
`y=18`

We get y =18.

Final answer:

`x=11,y=18.`