Question

if the perimeter of a rhombus is 64, what is the length of each side of the rhombus?
8
16
4
not enough information is given to answer the question.
question 5
find the values of x and y in the rhombus below.
x = 52,y = 10/3
x = 27,y = 10/3
x = 27,y = 10
x = 54,y = 10

Explanation:

1. For the first question:

Step1: Recall the property of a rhombus

A rhombus has 4 equal - length sides. Let the length of each side be \(s\). The perimeter \(P\) of a rhombus is given by \(P = 4s\).

Step2: Solve for the side - length

We know that \(P = 64\). Substituting into the formula \(P = 4s\), we get \(64=4s\). Solving for \(s\) by dividing both sides of the equation by 4, \(s=\frac{64}{4}=16\).

1. For the second question:

Step1: Use the property of a rhombus (equal sides)

In a rhombus, all sides are equal. So, if one side is \(2x - 1\) and another is \(53\), then \(2x-1 = 53\).
Add 1 to both sides: \(2x=53 + 1=54\).
Divide both sides by 2: \(x = 27\).
If one side is \(3y + 5\) and another side is \(35\), then \(3y+5 = 35\).
Subtract 5 from both sides: \(3y=35 - 5 = 30\).
Divide both sides by 3: \(y = 10\).

Answer:

1. For the first - question: B. 16
2. For the second - question: C. \(x = 27,y = 10\)