Question

AB = x + 20 DC = 5x AD = x − 2 BC = ? Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs. What is the length of BC?

Answer 1

`BC=3\ units`

Explanation:

we know that

In a parallelogram opposites sides are parallel and congruent

so

AB=DC

BC=AD

step 1

Find the value of x

we have

`AB=DC`

substitute the given values

`x+20=5x`

solve for x

`5x-x=20`

`4x=20`

`x=5`

so

`AB=x+20=5+20=25\ units`

`DC=5x=5(5)=25\ units`

step 2

Find the value of AD

`AD=x-2=5-2=3\ units`

Remember that

BC=AD

therefore

`BC=3\ units`