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A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 648 feet of fencing is used. Find the dimensions of the playground?
Without further information it is impossible to say what the dimensions are; only an equation can be given relating the width to length which will have infinitely many solutions as there are 2 unknowns: Let one dimension of the playground be x and the other be y; let the extra fence be constructed parallel to the side of length x. Then: total fence used = perimeter of rectangle + fence across the middle → 648 ft = 2x + 2y + x → 2y + 3x = 648 ft As we only have 1 equation but 2 unknowns, there are infinitely many possible solutions, eg: 2 ft wide by 321 ft long, split with a fence parallel to the 2 ft side; 4 ft wide by 318 ft long, split with a fence parallel to the 4 ft side; 129 ft wide by 130 ft long, split with a fence parallel to the 130 ft side. If the problem included other information, for example: the area of the playground is a maximum, then: From above: 2y + 3x = 648 → y = 324 - 3x/2 and area = xy → area = x(324 - 3x/2) → area = 324x - 3x²/2 To find the maximum area, completing the square gives: area = 3/2 (216x - x²) → area = -3/2 (x² - 216x) → area = -3/2 ((x - 108)² - 108²) → area = 3/2 (108² - (x - 108)²) As x varies (x - 108)² is greater than or equal to 0, and the greater it is the smaller the area is; the maximum area is when (x - 108)² is a minimum, ie: (x - 108)² = 0 → x - 108 = 0 → x = 108 → y = 324 - 3 × 108 / 2 = 162 Thus the maximum area is when the playground is 162 ft long by 108 ft wide with the dividing fence parallel to the 108 ft side.
If one side of an equilateral triangle is 12Cm find the Area?
Use Pythagoras' theorem to find the triangle's altitude or height: 122-62 = 108 and the square root of this is 10.39230485 1/2*base*height = area 1/2*6*10.39230485 = 31.17691455 square units
The sum of two positive integers is 108 one integer is three times as great as the other find the integers?
27 and 81; 27 + 81 = 108, and 3 x 27 = 81
What is the highest common factor of 48 and 108?
Find the prime factors of 48 and 108: 48 = 2*2*2*2*3 108 = 2*2*3*3*3 Now multiply the common factors: GCF = 2*2*3 = 12
What is the area of a rectangle with a diagonal of 15 and a length of 9?
Diagonal = 15 and Length = 9 units.Therefore, by Pythagoras, Breadth = sqrt(152 - 92) = sqrt(144) = 12 units.So area = 9*12 = 108 sq units.Diagonal = 15 and Length = 9 units.Therefore, by Pythagoras, Breadth = sqrt(152 - 92) = sqrt(144) = 12 units.So area = 9*12 = 108 sq units.Diagonal = 15 and Length = 9 units.Therefore, by Pythagoras, Breadth = sqrt(152 - 92) = sqrt(144) = 12 units.So area = 9*12 = 108 sq units.Diagonal = 15 and Length = 9 units.Therefore, by Pythagoras, Breadth = sqrt(152 - 92) = sqrt(144) = 12 units.So area = 9*12 = 108 sq units.
What is the area of a circle whose radius 108 inches?
Area of a circle is calculated by taking the radius squared times pi (3.14 approx.). 108 x 108 = 11,664 11,664 x 3.14 = 36,624.96 The area of a circle with a radius of 108 inches would be 36,624.96 square inches.
What's the radius for 108 feet?
The radius is half of the diameter. If 108 feet refers to the diameter of a circle, then the radius would be 108 feet divided by 2, which equals 54 feet.
What is the area of a 30 degree sector of a circle with a radius of 36?
Area of the circle = pi*362 = 1296*pi Area of the sector = 30/360 of 1296*pi = 108*pi square units
What is diameter of a circle with the radius of 54 inches?
The diameter is essentially twice the radius, so therefore a circle with a radius of 54 inches has a diameter of 108 inches.
What is the area of a circle if the diameter is 108 using 3.14 for pi?
The area of a circle if the diameter is 108 using 3.14 for pi is: 9,156.24 square units.
How many square feet in a 12 ft diameter circle?
Radius = diameter ÷ 2 Area = π x radius2 = π x (12 ÷ 2)2 = 36π ≈ 113 sq ft.
What is the radius of a circle if the area is 108cm?
You know that the formula of area for a circle is = pi * r^2 ... r being the radius. Therefore, you can plug it in to solve. pi * r^2 = 108. You need to isolate r, so you would divide by pi for both sides. r^2 = 34.378 . Then you can square root both sides r = 5.68 . Of course, I am rounding! So you if you want an exact answer, leave the pi sign!
What is the area of a parallelogram with a circle inside the base of the parallelogram is 9 and the diameter of the circle is 6?
Since the area of the circle would be multiplied due to the circumference of the pathogenic therum,so you would multiply 54x2=108.Then multiply that by 54,which is the absolute value of the area of the parallelogram,so 54x108,is 5832,which you'd find the square root of,76.4. :)
What is the diameter of a 54 inch circle?
It depends on what you mean by a certain size circle. If the certain size is the diameter, then the answer is 54 inches. If the certain size is the radius, then the answer is 108 inches. If the certain size is the circumference, then the answer is 54 / 3.14159 or about 17.19 inches
What is the accurate radius of the atom Xenon?
The atomic radius of Xenon is about 108 picometers (pm).
What is the volume in gallons of a cylinder with a radius of 108 inches and a height of 206 inches?
The volume of a cylinder with a radius of 108 inches and a height of 206 inches is 32,677.8 US gallons.
How do you find the measure of angle B in a circle where the angle is 108?
The answer depends on what angle B is and which angle is 108. And since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.
