Question

AB = x + 15 DC = 4x AD = x + 10 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=15\ units`

Explanation:

we know that

In a parallelogram opposite sides are congruent

In this problem

we have that

AB and DC are opposite sides

AD and BC are opposite sides

so

AB=DC

AD=BC

step 1

Find the value of x

AB=DC

substitute the given values

`x+15=4x`

solve for x

`4x-x=15`

`3x=15`

`x=5\ units`

step 2

Find the length of AD

we have that

`AD=x+10`

substitute the value of x

`AD=5+10=15\ units`

step 3

Find the length of BC

Remember that

AD=BC ----> by opposite sides

therefore

`BC=15\ units`