Question

ABCD is a parallelogram. if side AB=5x+7 side BC=8x-12 and side CD=7x-14 find the value of x

PLEASE HELP

Answer 1

The value of x is 10.5 units.

Explanation:

Given:

ABCD is a parallelogram.

AB =
`5x+7`

BC =
`8x-12`

CD =
`7x-14`

We need to find the value of x.

Now the Definition of Parallelogram states that;

"A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and the opposite angles are equal in measure."

Hence from Above definition we can say that;

`AB =CD` since these are the opposite sides of parallelogram.

Now Substituting the given values we get;

`5x+7=7x-14`

Now solving the equation we get;

Combining the like terms first.

`7x-5x=7+14`

Now using addition and subtraction property of equality we get;

`2x=21`

Now using Division Property we will divide 2 on both side we get;

`(2x)/(2)=(21)/(2)\\\\x=10.5 \ units`

Hence the value of x is 10.5 units.