Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A rectangular front porch has an area of 6060 square feet. Its perimeter is 3232 feet. What are the dimensions of the porch?\newline___\_\_\_ feet by ___\_\_\_ feet

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Area and perimeter: word problemsright chevron icon

Full solution

Q. A rectangular front porch has an area of 6060 square feet. Its perimeter is 3232 feet. What are the dimensions of the porch?\newline___\_\_\_ feet by ___\_\_\_ feet
  1. Define Area Equation: Let's denote the length of the porch as LL feet and the width as WW feet. We know that the area (AA) of a rectangle is given by the formula A=L×WA = L \times W. We are given that the area is 6060 square feet.\newlineSo, we have the equation:\newlineL×W=60L \times W = 60
  2. Define Perimeter Equation: We also know that the perimeter PP of a rectangle is given by the formula P=2L+2WP = 2L + 2W. We are given that the perimeter is 3232 feet.\newlineSo, we have the equation:\newline2L+2W=322L + 2W = 32
  3. Simplify Perimeter Equation: To find the dimensions LL and WW, we need to solve these two equations together. Let's simplify the perimeter equation by dividing all terms by 22 to make it easier to work with:\newlineL+W=16L + W = 16
  4. Express WW in Terms of LL: Now we have a system of two equations:\newline11) L×W=60L \times W = 60\newline22) L+W=16L + W = 16\newlineWe can solve this system by expressing one variable in terms of the other using the second equation. Let's express WW in terms of LL:\newlineW=16−LW = 16 - L
  5. Substitute WW into Area Equation: Substitute W=16−LW = 16 - L into the first equation (L×W=60L \times W = 60):\newlineL×(16−L)=60L \times (16 - L) = 60\newlineExpand the equation:\newline16L−L2=6016L - L^2 = 60
  6. Rearrange Equation to Quadratic: Rearrange the equation to form a quadratic equation: L2−16L+60=0L^2 - 16L + 60 = 0
  7. Solve Quadratic Equation: Now we need to solve the quadratic equation for LL. We can do this by factoring, completing the square, or using the quadratic formula. The equation looks like it can be factored:\newline(L−10)(L−6)=0(L - 10)(L - 6) = 0
  8. Find Possible Values for L: Setting each factor equal to zero gives us the possible values for L:\newlineL−10=0L - 10 = 0 or L−6=0L - 6 = 0\newlineSo, L=10L = 10 or L=6L = 6
  9. Calculate Possible Dimensions: If L=10L = 10, then W=16−L=16−10=6W = 16 - L = 16 - 10 = 6. If L=6L = 6, then W=16−L=16−6=10W = 16 - L = 16 - 6 = 10. Since a rectangle's length and width are interchangeable, we have two possible sets of dimensions that satisfy both the area and perimeter: 1010 feet by 66 feet or 66 feet by 1010 feet.

More problems from Area and perimeter: word problems

Question
The work done by stretching a certain spring increases by 0.13x 0.13 x joules per centimeter (where x x is the displacement, in centimeters, beyond the spring's natural length).\newlineHow much work (in Joules) must be done in order to stretch the spring from x=4 x=4 to x=10 x=10 ?\newlineChoose 11 answer:\newline(A) 55.4646\newline(B) 77.5454\newline(C) 10.92 \mathbf{1 0 . 9 2} \newline(D) 15.08 \mathbf{1 5 . 0 8}
Get tutor helpright-arrow

Posted 9 months ago

Question
Ahmed is modeling the area covered by a moss using the following equation:\newlineA=t2+5.8t+9.41 A=t^{2}+5.8 t+9.41 \newlinewhere A A is the area covered in square centimeters, negative values of t t represent a number of days before noon on July 11 , 20142014 , and positive values of t t represent a number of days after noon on July 11,20142014 . Which of the following equivalent expressions contains the number of days before noon on July 11,20142014 , as a constant or coefficient, when the moss started with its smallest area of 11 square centimeter?\newlineChoose 11 answer:\newline(A) (t−(−2.9))2+1 (t-(-2.9))^{2}+1 \newline(B) (t−(−1))2+3.8t+8.41 (t-(-1))^{2}+3.8 t+8.41 \newline(C) (t−(−3.9))(t−(−1.9))+2 (t-(-3.9))(t-(-1.9))+2 \newline(D) t(t−(−5.8))+9.41 t(t-(-5.8))+9.41
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve.\newlineFind the exact volume and surface area of a sphere of radius 1212 inches.\newlineV=576π cu in.;V=576\pi\text{ cu in.}; SA=2304π sq in.SA=2304\pi\text{ sq in.}\newlineV=2304π cu in.;V=2304\pi\text{ cu in.}; SA=576π sq in.SA=576\pi\text{ sq in.}\newlineV=1728π cu inV=1728\pi\text{ cu in} ;SA=144π sq in.;SA=144\pi\text{ sq in.}\newlineV=6912π cuin.:V=6912\pi\text{ cuin.}:SA⋅=36π sq in.SA^{\cdot}=36\pi\text{ sq in.}\newline
Get tutor helpright-arrow

Posted 8 months ago

Question
What is the height of the tent?
Get tutor helpright-arrow

Posted 8 months ago

Question
The volume of a rectangular prism is 108 cm3 108 \mathrm{~cm}^{3} . Eric measures the sides to be 3.32 cm 3.32 \mathrm{~cm} by 4.04 cm 4.04 \mathrm{~cm} by 8.72 cm 8.72 \mathrm{~cm} . In calculating the volume, what is the relative error, to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 8 months ago

Question
In △UVW,w=8.9 \triangle \mathrm{UVW}, w=8.9 inches, v=9 v=9 inches and ∠V=50∘ \angle \mathrm{V}=50^{\circ} . Find all possible values of ∠W \angle \mathrm{W} , to the nearest 1010th of a degree.\newlineAnswer:
Get tutor helpright-arrow

Posted 8 months ago

Question
Circle O O shown below has a radius of 77 inches. To the nearest tenth of an inch, determine the length of the arc, x x , subtended by an angle of 11.44 radians.\newlineAnswer: □\square inches
Get tutor helpright-arrow

Posted 8 months ago

Question
Circle O O shown below has an arc of length 1919 inches subtended by an angle of 11 radians. Find the length of the radius, x x , to the nearest tenth of an inch.\newlineAnswer: □\square inches
Get tutor helpright-arrow

Posted 8 months ago

Question
The area of a rectangular goat pen is 54 square meters54 \, \text{square meters}. The perimeter is 30 meters30 \, \text{meters}. What are the dimensions of the pen?\newline____\_\_\_\_ meters by ____\_\_\_\_ meters
Get tutor helpright-arrow

Posted 8 months ago

Question
The perimeter of a square piece of tissue paper is 3636 centimeters. How long is each side of the tissue paper?\newline​_____ centimeters
Get tutor helpright-arrow

Posted 8 months ago

View all (10)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant