Draw a rectangle of perimeter 30cm and length of sides in the ratio 1:2.draw two more rectangles of the same perimeter with the length of sides in the ratio 2:3 and 3:7 compute the areas of all three rectangles?
good job, except that 2(6+12) = 36, not 30
Should have been
2(x) + 2(2x) = 30
6x = 30
x = 5
sides are 5 cm and 10 cm, with an area of 50 cm^2, and a perimeter of 2(5+10) = 30
Perimeter=30 cms
Ratio of sides=2:3
Breadth=2+3=5 cms
=(2÷5)×30=2×30=60÷5=12 cms
=12÷2=6 cms is the breadth
Length=3×30=90÷5=18 cms
=18÷2=9 cms is the length
Well, I hate to break it to you, but as much as I love making jokes, I can't draw anything for you. However, I can help you with the math!
Rectangle 1:
Let the length of one side of the rectangle be x cm. Then, the other side would be 2x cm. The perimeter of the rectangle is given as 30 cm.
Perimeter = 2(length + width)
30 = 2(x + 2x)
30 = 2(3x)
30 = 6x
x = 5 cm
So, the length of the rectangle is 5 cm and the width is 2 * 5 = 10 cm.
Now, we can calculate the area of Rectangle 1:
Area = length * width
Area = 5 cm * 10 cm
Area = 50 cm²
Rectangle 2:
In this case, let the length of one side be 2x cm and the other side be 3x cm. The perimeter is still 30 cm.
Perimeter = 2(length + width)
30 = 2(2x + 3x)
30 = 10x
x = 3 cm
So, the length of the rectangle is 2 * 3 cm = 6 cm and the width is 3 * 3 cm = 9 cm.
The area of Rectangle 2 is:
Area = length * width
Area = 6 cm * 9 cm
Area = 54 cm²
Rectangle 3:
For this rectangle, let one side be 3x cm and the other side be 7x cm. The perimeter is still 30 cm.
Perimeter = 2(length + width)
30 = 2(3x + 7x)
30 = 20x
x = 1.5 cm
The length of the rectangle is 3 * 1.5 cm = 4.5 cm and the width is 7 * 1.5 cm = 10.5 cm.
The area of Rectangle 3 is:
Area = length * width
Area = 4.5 cm * 10.5 cm
Area ≈ 47.25 cm²
So, the areas of the three rectangles are:
Rectangle 1: 50 cm²
Rectangle 2: 54 cm²
Rectangle 3: 47.25 cm²
I hope these calculations didn't draw you into a rectangle of confusion!
To solve this problem, let's start by finding the dimensions of the first rectangle with sides in a ratio of 1:2.
Let the length of one side be x cm. Since the sides are in a ratio of 1:2, the length of the other side will be 2x cm.
The perimeter of the rectangle is given as 30 cm. Perimeter is the sum of all sides of a shape.
So, the perimeter of the rectangle can be expressed as:
Perimeter = 2(length + width)
Substituting the values, we get:
30 = 2(x + 2x)
30 = 6x
x = 5 cm
Therefore, the dimensions of the first rectangle are 5 cm and 10 cm.
Now, let's move on to the second rectangle with sides in a ratio of 2:3.
Let the length of one side be x cm. The length of the other side will be 3x cm.
Using the same formula for perimeter, we can set up the equation:
30 = 2(x + 3x)
30 = 8x
x = 3.75 cm
Therefore, the dimensions of the second rectangle are 3.75 cm and 11.25 cm.
Lastly, let's find the dimensions of the third rectangle with sides in a ratio of 3:7.
Let the length of one side be x cm. The length of the other side will be 7x cm.
Again, using the same perimeter formula, we have:
30 = 2(x + 7x)
30 = 16x
x = 1.875 cm
Therefore, the dimensions of the third rectangle are 1.875 cm and 13.125 cm.
Now, we can calculate the areas of all three rectangles using the formula:
Area = length * width
For the first rectangle:
Area = 5 cm * 10 cm = 50 cm²
For the second rectangle:
Area = 3.75 cm * 11.25 cm = 42.1875 cm²
For the third rectangle:
Area = 1.875 cm * 13.125 cm = 24.609375 cm²
So, the areas of the three rectangles are 50 cm², 42.1875 cm², and 24.609375 cm² respectively.
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I will do the first one, you do the other two in the same way.
let the width be x
let the length be 2x, notice x : 2x = 1 : 2
2(x) + 2(2x) = 30
5x = 30
x = 6
sides are 6 cm and 12 cm, with an area of 72 cm^2