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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.
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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.
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 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
How do you find the perimeter of a rectangle using subtraction?
i dont no if you can find the perimeter of a triagle by using subtration the formula is adding all the up together.
What are the dimensions of a rectangle that has a perimeter of 29 cm and an area of 50.3125 square cm?
Let the dimensions be x and y:- If: 2x+2y = 29 then y =14.5-x If: xy = 50.3125 then x(14.5-x) = 50.3125 Expanding brackets and transposing terms: 14.5x -x^2 -50.3125 = 0 Using the quadratic equation formula: x = 8.75 or x = 5.75 Therefore dimensions of the rectangle are: length = 8.75 cm and width = 5.75 cm Check: 2(8.75+5.75) = 29 cm Check: 8.75*5.75 = 50.3125 square cm
