Question

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

Answer 1

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 $434\ units$

Answer 2

The value of s is 45 and the length of side BC is; 434.

What is a Rhombus?

A rhombus is a plane shape of the form given I'm the attached image with all its sides equal.

Hence,

• AB = BC = CD = DA

To determine the value of s;

• 10s - 16 = 9s + 29

• 10s-9s = 29+16

• s = 45.

The length of side BC = CD = 10(45) - 16 = 450 - 16

The length of side BC = 450 -16 = 434

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