Draw an L-shaped room with an area of 20 m2 and a perimeter of 24 m. Show all the measurements. Explain your working.
This is hard to explain in words.
That's why in google paste:
math L-shaped room calculator
When you see list of results click on:
L-Shape - Geometry Calculator - Rechneronline
When page be open in rectangle: Long outer side (a)
type 8
In rectangle: Short outer side (b):
type 4
In rectangle: Width (c):
type 2
and click Calculate
You will see solution with formulas.
To draw an L-shaped room with an area of 20 m2 and a perimeter of 24 m, we need to determine the dimensions of the room.
Let's assume the longer side of the L-shaped room measures x meters, and the shorter side measures y meters.
Given that the area of the room is 20 m2, we have the equation:
x * y = 20 Equation 1
Given that the perimeter of the room is 24 m, we have the equation:
2x + 2y = 24 Equation 2
To solve this system of equations, we can rearrange Equation 2 to isolate one variable in terms of the other:
y = 12 - x Equation 3
Now substitute Equation 3 into Equation 1:
x * (12 - x) = 20
Expanding the equation:
12x - x^2 = 20
Rearranging terms:
x^2 - 12x + 20 = 0
Using the quadratic formula to solve for x:
x = (-(-12) ± √((-12)^2 - 4 * 1 * 20)) / (2 * 1)
x = (12 ± √(144 - 80)) / 2
x = (12 ± √64) / 2
x = (12 ± 8) / 2
For the positive solution:
x = (12 + 8) / 2
x = 20 / 2
x = 10
Now substitute x = 10 into Equation 3 to find y:
y = 12 - x
y = 12 - 10
y = 2
So, the longer side of the L-shaped room measures 10 meters, and the shorter side measures 2 meters. Now let's draw the room:
```
________
| |
y | |
|_ _|____
x
```
In this drawing, the longer side (x) is 10 meters and the shorter side (y) is 2 meters.
To draw an L-shaped room with an area of 20 m² and a perimeter of 24 m, let's follow these steps:
Step 1: Understand the L-shape Room
An L-shaped room consists of two perpendicular sections, forming a right-angle corner. To calculate the area and perimeter, we need to split the room into two rectangular sections, one longer and one shorter.
Step 2: Assign Variables
Let's assign variables to the dimensions of the room:
- Length of the longer section: L meters
- Width of the longer section: W meters
- Length of the shorter section: L meters
- Width of the shorter section: W - L meters (since it is smaller in length)
Step 3: Determine the Formulas
The formulas we will use to calculate the area and perimeter are:
- Area: Area = Length × Width
- Perimeter: Perimeter = 2 × (Length + Width)
Step 4: Set Up Equations
From the problem statement, we know that the total perimeter is 24 m. Substituting the variables into the perimeter formula, we get:
Perimeter = 2 × (L + W) = 24
From the problem statement, we also know that the total area is 20 m². Substituting the variables into the area formula, we get:
Area = L × W = 20
Step 5: Solve Equations
To draw the specific L-shaped room with the given area and perimeter, we need to solve the equations we set up.
First, solve the perimeter equation:
2 × (L + W) = 24
L + W = 12
Next, solve the area equation:
L × W = 20
To find specific measurements, we can use algebra, trial and error, or other mathematical techniques. Solving equation systems is typically done using algebra.
Let's assume one solution that satisfies both equations is L = 4 meters and W = 8 meters. The sum of L and W is 12 (L + W = 4 + 8 = 12), and the product of L and W is 32 (L × W = 4 × 8 = 32).
Step 6: Draw the L-shaped Room
Now that we have the dimensions, we can draw the L-shaped room.
The longer section has a length of 4 meters and a width of 8 meters. Place this rectangle vertically or horizontally, depending on your preference.
The shorter section has a length of 4 meters (the same as the longer section) and a width of 8 - 4 = 4 meters.
Position the shorter section to create a right-angle corner, connecting one edge of the longer section.
The room should now resemble a capital letter "L," with dimensions labeled accordingly.
I hope this explanation helps you understand how to draw an L-shaped room with the given area and perimeter!