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Interesting one!
If a rectangle has width w and height h,
1) the area a = wh
2) the perimeter p = 2w + 2h
From 1), w=a/h
Substituting into 2)
p = 2a/h + 2h
Multiplying by h
pH = 2a + 2h2
Rearranging
2h2 - pH + 2a = 0 This is a quadratic equation in h.
Factorising, using the standard quadratic formula,
h = (p ± sqrt(p2 - 16a))/4
The two solutions to this will be the two dimensions.
What else can I help you with?
What is the formual of a rectangle?
The formula for the area of a rectangle is given by ( A = l \times w ), where ( A ) represents the area, ( l ) is the length, and ( w ) is the width. The perimeter of a rectangle can be calculated using the formula ( P = 2l + 2w ), where ( P ) is the perimeter. These formulas help determine the size and boundary of a rectangle based on its dimensions.
What is the perimeter of the rectangle with a length of 8 inches is 48 square inches?
You must first calculate the width, using the formula for the area of a rectangle (plug in the numbers you know into the formula, and solve for width). Once you know this, you can plug in the numbers in the formula for a rectangle's perimeter.
How do you write an algorithm of perimeter of a rectangle?
To write an algorithm for calculating the perimeter of a rectangle, you start by defining the inputs, which are the length (L) and width (W) of the rectangle. The perimeter (P) can be calculated using the formula ( P = 2 \times (L + W) ). The steps in the algorithm would include: 1) Input the values of L and W, 2) Calculate the perimeter using the formula, and 3) Output the result.
Do all rectangles have even perimeters?
No, not all rectangles have even perimeters. The perimeter of a rectangle is calculated using the formula ( P = 2(length + width) ). If either the length or width is an odd number, their sum can be odd, resulting in an odd perimeter when multiplied by 2. Therefore, a rectangle can have an odd perimeter if one or both dimensions are odd.
What is a rectangle with a perimeter of 10 units?
A rectangle with a perimeter of 10 units has a total distance around its edges equal to 10 units. The perimeter ( P ) of a rectangle is calculated using the formula ( P = 2(l + w) ), where ( l ) is the length and ( w ) is the width. Therefore, ( l + w = 5 ). Possible dimensions for such a rectangle could be ( (1, 4) ), ( (2, 3) ), or any other pair of positive numbers that sum to 5.
What is the formual of a rectangle?
The formula for the area of a rectangle is given by ( A = l \times w ), where ( A ) represents the area, ( l ) is the length, and ( w ) is the width. The perimeter of a rectangle can be calculated using the formula ( P = 2l + 2w ), where ( P ) is the perimeter. These formulas help determine the size and boundary of a rectangle based on its dimensions.
What is the perimeter of the rectangle with a length of 8 inches is 48 square inches?
You must first calculate the width, using the formula for the area of a rectangle (plug in the numbers you know into the formula, and solve for width). Once you know this, you can plug in the numbers in the formula for a rectangle's perimeter.
How do you write an algorithm of perimeter of a rectangle?
To write an algorithm for calculating the perimeter of a rectangle, you start by defining the inputs, which are the length (L) and width (W) of the rectangle. The perimeter (P) can be calculated using the formula ( P = 2 \times (L + W) ). The steps in the algorithm would include: 1) Input the values of L and W, 2) Calculate the perimeter using the formula, and 3) Output the result.
What shape has an area of 12 and a perimeter of 16?
The shape that has an area of 12 and a perimeter of 16 is a rectangle. To find the dimensions of the rectangle, you can set up equations using the formulas for area and perimeter. Let the length of the rectangle be L and the width be W. The equations would be: 2L + 2W = 16 (perimeter) and LW = 12 (area). Solving these equations simultaneously will give you the dimensions of the rectangle.
What is the area of 12 cm2 and the perimeter of 14 cm?
Well, honey, if the area is 12 cm² and the perimeter is 14 cm, that means we're dealing with a rectangle. To find the dimensions, you'll need to do some math. Let's break out the algebra and solve for the sides like the math whiz you are.
Draw a flowchart that will compute and display the Area of a rectangle using the formula: Area = Length Width?
The formula for the perimeter of a rectangle is: p = 2(l + w) In other words, just add all four sides. You can't calculate the perimeter of the rectangle if you know only the length.
Do all rectangles have even perimeters?
No, not all rectangles have even perimeters. The perimeter of a rectangle is calculated using the formula ( P = 2(length + width) ). If either the length or width is an odd number, their sum can be odd, resulting in an odd perimeter when multiplied by 2. Therefore, a rectangle can have an odd perimeter if one or both dimensions are odd.
What is a rectangle with a perimeter of 10 units?
A rectangle with a perimeter of 10 units has a total distance around its edges equal to 10 units. The perimeter ( P ) of a rectangle is calculated using the formula ( P = 2(l + w) ), where ( l ) is the length and ( w ) is the width. Therefore, ( l + w = 5 ). Possible dimensions for such a rectangle could be ( (1, 4) ), ( (2, 3) ), or any other pair of positive numbers that sum to 5.
If farmer Dan has 100 feet of fencing write an inequality to find the dimensions of the rectangle with the largest perimeter that can be created using 100 feet of fencing?
To find the dimensions of a rectangle with the largest perimeter using 100 feet of fencing, we can express the perimeter ( P ) of a rectangle in terms of its length ( l ) and width ( w ) as ( P = 2l + 2w ). Since the total amount of fencing is 100 feet, we set up the inequality ( 2l + 2w \leq 100 ). Simplifying this gives ( l + w \leq 50 ). The dimensions that maximize the area (which is a related concept) would be when ( l = w = 25 ) feet, creating a square shape.
What are the dimensions of a rectangle that has a perimeter of 19.8 cm and an area of 24.3 square cm showing work?
Divide the perimeter by 2 then find two numbers that have a sum of 9.9 and a product of 24.3 which will work out as 5.4 and 4.5 by using the quadratic equation formula. Check: 2*(5.4+4.5) = 19.8 cm which is the perimeter Check: 5.4*4.5 = 24.3 square cm which is the area Therefore the dimensions of the rectangle are: 5.4 cm and 4.5 cm
The perimeter of a rectangle is 72m the width of the rectangle is 16m what is the area of the rectangle?
To find the area of a rectangle, you need to know the formula: Area = length x width. Given that the perimeter is 72m and the width is 16m, we can calculate the length by using the formula for perimeter of a rectangle: Perimeter = 2(length + width). Substituting the values we have, 72 = 2(length + 16), which simplifies to length + 16 = 36. Therefore, the length of the rectangle is 20m. Finally, the area of the rectangle is 20m x 16m = 320 square meters.
What is the area of a rectangle if the perimeter is 24 units?
To find the area of a rectangle with a perimeter of 24 units, we can use the formula for perimeter: ( P = 2(l + w) ), where ( l ) is the length and ( w ) is the width. This gives us ( l + w = 12 ). The area ( A ) is calculated using ( A = l \times w ). The maximum area occurs when the rectangle is a square, leading to dimensions of 6 units by 6 units, resulting in an area of 36 square units.
