Question

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

Answer 1

Answer:

The value of x is 10.5 units.

Step-by-step 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;

$\frac{2x}{2}=\frac{21}{2}\\\\x=10.5 \ units$

Hence the value of x is 10.5 units.