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Where:
– a is the breadth
– b is the length
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A rectangle is a four-sided polygon with opposite sides being equal in length and all angles being right angles. In a rectangle, the length is typically denoted by "b" and the width is denoted by "a".
The formula for calculating the perimeter of a rectangle is given by:
P = 2a + 2b
where P represents the perimeter, a represents the width, and b represents the length of the rectangle.
The formula for calculating the area of a rectangle is given by:
A = ab
where A represents the area of the rectangle, a represents the width, and b represents the length of the rectangle.
Moreover, the formula for calculating the diagonal of a rectangle is given by the Pythagorean theorem:
c = \sqrt{a^2 + b^2}
where c represents the diagonal, a represents the width, and b represents the length of the rectangle.
AÂ rectangle with a length of b and width of a can be characterized by its perimeter, area, and diagonal using the formulas provided above.
1. What is the perimeter of a rectangle with length b and width a?
P = 2(a + b)
Step by step solution:
Given that the length of the rectangle is b and the width is a, we know that the perimeter is the sum of all sides.
Therefore, the perimeter, P, is equal to twice the sum of the length and width,
so P = 2(a + b) .
2. Find the area of a rectangle with length b and width a.
A = ab
Step by step solution:
The area of a rectangle is the product of length and width. Thus, the area, A, is given by A = ab .
3. Determine the diagonal of a rectangle with length b and width a.
D = \sqrt{a^2 + b^2}
Step by step solution:
The diagonal of a rectangle can be found using the Pythagorean theorem.
By considering the length and width as the two sides of a right-angled triangle, the square of the diagonal is equal to the sum of the squares of the length and width.
Therefore, the diagonal, D, can be calculated as
D = \sqrt{a^2 + b^2} .
4. Given a rectangle with a diagonal of length D and width a, find the length b of the rectangle.
b = \sqrt{D^2 - a^2}
Step by step solution:
To find the length of the rectangle with a given diagonal and width, we can rearrange the Pythagorean theorem formula. By substituting the width a and diagonal D, we have b = \sqrt{D^2 - a^2} .
5. Suppose a rectangle has a perimeter of 20 units, with a length b of 6 units. Calculate the width a of the rectangle.
a = \dfrac{20 - 2b}{2}
Step by step solution:
Given that the perimeter P of the rectangle is 20 units, and the length b is 6 units, we can find the width a by rearranging the formula for the perimeter.
Thus, the width a is calculated as
a = \dfrac{20 - 2b}{2} .
1. What is the perimeter of a rectangle with length b and width a?
P = 2a + 2b
2. What is the area of a rectangle with length b and width a?
A = ab
3. If the length of a rectangle is 5 and the width is 3, what is the perimeter?
P = 2(3) + 2(5) = 16
4. If the length of a rectangle is 8 and the perimeter is 30, what is the width?
30 = 2w + 2(8) \implies w = 7
5. If the area of a rectangle is 24 and the width is 4, what is the length?
24 = 4b \implies b = 6
6. If the perimeter of a rectangle is 28 and the width is 4, what is the length?
28 = 2b + 2(4) \implies b = 10
7. If the area of a rectangle is 45 and the width is 5, what is the length?
45 = 5b \implies b = 9
8. What is the width of a rectangle with length 10 and area 100?
100 = 10a \implies a = 10
9. If the perimeter of a rectangle is 24 and the length is 6, what is the width?
24 = 2w + 2(6) \implies w = 6
10. If the area of a rectangle is 35 and the length is 7, what is the width?
35 = 7b \implies b = 5
11. If the perimeter of a rectangle is 40 and the width is 8, what is the length?
40 = 2a + 2(8) \implies a = 12
12. What is the area of a rectangle with length 9 and perimeter 34?
34 = 2a + 2b \implies ab = 45
13. If the perimeter of a rectangle is 18 and the length is 3, what is the width?
18 = 2w + 2(3) \implies w = 6
14. If the area of a rectangle is 56 and the width is 8, what is the length?
56 = 8a \implies a = 7
15. If the perimeter of a rectangle is 25 and the width is 5, what is the length?
25 = 2a + 2(5) \implies a = 7.5
