Area of rhombus is 480cm² and one of its diagonal is 48cm find: 1.the length of other diagonal.
2.each side.
3.perimeter
4.the distance between it's side

Given that the area of a rhombus is 480 cm² and one of its diagonals is 48 cm, we need to find the following:

### 1. Length of the Other Diagonal

The area \( A \) of a rhombus can be calculated using the formula:
\[
A = \frac{1}{2} \times d_1 \times d_2
\]
where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.

We know:
\[
480 = \frac{1}{2} \times 48 \times d_2
\]

To find \( d_2 \):
\[
d_2 = \frac{2 \times 480}{48} = \frac{960}{48} = 20 \text{ cm}
\]

### 2. Length of Each Side

The length of a side \( s \) of the rhombus can be calculated using the relationship between the diagonals and the sides:
\[
s = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2}
\]
Substituting the values \( d_1 = 48 \) cm and \( d_2 = 20 \) cm:
\[
s = \sqrt{\left(\frac{48}{2}\right)^2 + \left(\frac{20}{2}\right)^2} = \sqrt{24^2 + 10^2} = \sqrt{576 + 100} = \sqrt{676} = 26 \text{ cm}
\]

### 3. Perimeter of the Rhombus

The perimeter \( P \) of a rhombus is given by:
\[
P = 4 \times s
\]
So, substituting the value of \( s = 26 \) cm:
\[
P = 4 \times 26 = 104 \text{ cm}
\]

### 4. Distance Between Its Sides

The distance between the sides (also known as the height \( h \)) can be found using the area formula for the rhombus:
\[
A = s \times h
\]
Rearranging to find \( h \):
\[
h = \frac{A}{s} = \frac{480}{26} \approx 18.46 \text{ cm}
\]

### Summary of Results
1. Length of the other diagonal \( d_2 = 20 \) cm.
2. Length of each side \( s = 26 \) cm.
3. Perimeter of the rhombus \( P = 104 \) cm.
4. Distance between the sides (height) \( h \approx 18.46 \) cm.

Would you like any more details, or do you have any questions?

---

Here are 5 related questions to further your understanding:
1. How would the area change if the other diagonal was doubled?
2. What is the relationship between the diagonals and the area of a rhombus?
3. How does the perimeter of a rhombus compare to its diagonals?
4. What are the properties of a rhombus that distinguish it from other quadrilaterals?
5. How would you find the area if both diagonals were unknown?

**Tip:** Remember that the diagonals of a rhombus bisect each other at right angles, forming four right-angled triangles within the rhombus.

Explore how to solve a problem involving a rhombus with an area of 480cm² and one diagonal of 48cm. Find the length of the other diagonal, each side length, perimeter, and the distance between its sides. Understand the geometric properties of rhombus and apply the area formula and perimeter calculation. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation