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What are the new dimensions of a 7 by 3 rectangle when its dimensions are increased by equal amounts giving an extra 85.25 square cm to its area showing work?
Wiki User
∙ 12y ago
This sounds kind of like a homework problem. I assume the dimensions are 7 cm by 3 cm to start with. The original area is (7 cm)(3 cm) = 21 cm². The final area is 21 cm² + 85.25 cm² = 106.25 cm². Increase each dimension by the same amount:
(7 + x)(3 + x) = 106.25 ---> 21 + 10x + x² = 106.25 ---> x² + 10x - 85.25 = 0 Solve this quadratic (I used the quadratic formula) x = 5.5 or -15.5. So we cannot have a negative dimension, so add 5.5 cm to each dimension. Check it out with (12.5 cm)(8.5 cm) = 106.25 cm²
Wiki User
∙ 12y ago
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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
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I suggest that you do the following:* Convert the meters to centimeters, to have compatible units.* Write the equation for the area of the rectangle. Replace the variable "a" (area) with the known area.* Write the equation for the perimeter of a rectangle. Replace the variable for the perimeter with the known perimeter (in cm).* Use any method to solve the simultaneous equations.Another Answer:-Let the dimensions be x and yIf: 2x+2y = 100 then x+y = 50 and x = 50-yIf: xy = 600 then (50-y)y = 600 and so 50y-y2-600 = 0Solving the quadratic equation: y = 20 or y = 30Therefore by substitution the dimensions are: when y = 20 cm then x = 30 cm
What are the dimensions of a rectangle when one side is 3 cm longer than the other side and its area is twice its perimeter in square cm showing work with answers?
Let the dimensions be x and x+3 Perimeter: 4x+6 Area: x(x+3) = 2(4x+6) => x^2 +3x = 8x+12 => x^2 -5x-12 = 0 Solving the above quadratic equation: x has a positive value of 6.77 rounded to 2dp Therefore dimensions are: 6.77 cm and 9.77 cm
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Well, you can do your own homework, but here is the general outline of what you must do. Use the variable "x" to express the width of the rectangle. In that case, because of the ratio, the length will be (4/3)x. Write an equation for the area of the rectangle, replace x, (4/3)x and the known area, and solve for "x". (Since a quadratic equation will give you two solutions, you will obviously accept the positive solution.) Once you calculate "x", you can easily calculate the other side of the rectangle, as (4/3)x. Finally, use the Pythagorean Theorem to calculate the diagonal. Another Answer:- 1 Let the dimensions be 3x and 4x 2 So 3x*4x = 369.63 or 12x2 = 369.63 3 Divide each side by 12 and then square root each side 4 Therefore: x = 5.55 and dimensions must be 16.65 by 22.2 5 Using Pythagoras: 16.652+22.22 = 756.9025 and its square root is 27.75 6 Answer: length of diagonal = 27.75 cm
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
What are the dimensions of a rectangle that has an area of 600 square cm and a perimeter of 1 m showing work?
I suggest that you do the following:* Convert the meters to centimeters, to have compatible units.* Write the equation for the area of the rectangle. Replace the variable "a" (area) with the known area.* Write the equation for the perimeter of a rectangle. Replace the variable for the perimeter with the known perimeter (in cm).* Use any method to solve the simultaneous equations.Another Answer:-Let the dimensions be x and yIf: 2x+2y = 100 then x+y = 50 and x = 50-yIf: xy = 600 then (50-y)y = 600 and so 50y-y2-600 = 0Solving the quadratic equation: y = 20 or y = 30Therefore by substitution the dimensions are: when y = 20 cm then x = 30 cm
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When children demonstrate conservation they are showing understanding?
differences in appearance do not affect total amounts
What are the dimensions of a rectangle when one side is 3 cm longer than the other side and its area is twice its perimeter in square cm showing work with answers?
Let the dimensions be x and x+3 Perimeter: 4x+6 Area: x(x+3) = 2(4x+6) => x^2 +3x = 8x+12 => x^2 -5x-12 = 0 Solving the above quadratic equation: x has a positive value of 6.77 rounded to 2dp Therefore dimensions are: 6.77 cm and 9.77 cm
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A balanced equation is representative for the amounts and nature for reactants and products involved.
What are a penny's dimensions?
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What is the length of the diagonal of a rectangle whose dimensions are in the ratio of 3 to 4 with with an area of 369.63 square cm showing work?
Well, you can do your own homework, but here is the general outline of what you must do. Use the variable "x" to express the width of the rectangle. In that case, because of the ratio, the length will be (4/3)x. Write an equation for the area of the rectangle, replace x, (4/3)x and the known area, and solve for "x". (Since a quadratic equation will give you two solutions, you will obviously accept the positive solution.) Once you calculate "x", you can easily calculate the other side of the rectangle, as (4/3)x. Finally, use the Pythagorean Theorem to calculate the diagonal. Another Answer:- 1 Let the dimensions be 3x and 4x 2 So 3x*4x = 369.63 or 12x2 = 369.63 3 Divide each side by 12 and then square root each side 4 Therefore: x = 5.55 and dimensions must be 16.65 by 22.2 5 Using Pythagoras: 16.652+22.22 = 756.9025 and its square root is 27.75 6 Answer: length of diagonal = 27.75 cm
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