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

Answer:

$BC=15\ units$

Step-by-step 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

$BC=15\ units$