Question

What is the value of s and the length of side BC if ABCD is a rhombus?

Answer 1

The rhombus has four equal sides

10s - 16 = 9s + 29
10s - 9s = 29 + 16
s = 45

BC = CD = 10s-16 = 10*45 - 16 = 434

Answer 2

Step 1

Find the value of s

we know that

In a Rhombus all sides are congruent

so

$AB=BC=CD=DA$

$AB=9s+29\\CD=10s-16$

equate AB and CD

$9s+29=10s-16$

Combine like term

$10s-9s=29+16$

$s=45\ units$

The answer Part a) is

the value of s is $45\ units$

Step 2

Find the value of side AB

$AB=9s+29$

substitute the value of s

$AB=9*45+29=434\ units$

Remember that the sides are congruent

$AB=BC=CD=DA$

therefore

the answer Part b) is

The length of the side BC is $434\ units$