Square vs rectangle

Square and rectangle have the same area contents. The length of the rectangle is 9 greater and width 6 less than side of the square. Calculate the side of a square.

Result

a =  18

Solution:

S1=S2 a2=(a+9)(a−6) a2=a2+9a−6a−9⋅ 6 3a=9⋅ 6=18 a=9⋅ 6/3=18 S1=a2=182=324 S2=(a+9)⋅ (a−6)=(18+9)⋅ (18−6)=324S_{1}=S_{2} \ \\ a^2=(a+9)(a-6) \ \\ a^2=a^2+9a-6a-9 \cdot \ 6 \ \\ 3a=9 \cdot \ 6=18 \ \\ a=9 \cdot \ 6/3=18 \ \\ S_{1}=a^2=18^2=324 \ \\ S_{2}=(a+9) \cdot \ (a-6)=(18+9) \cdot \ (18-6)=324

Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Do you want to convert length units?

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  1. Square and rectangle
    ctverec Calculate the side of a square which content area equals area of the rectangle having a length of 3 cm greater and by 2 cm smaller than the side of the square.
  2. A photograph
    photo A photograph will stick to a white square letter with a x cm length. The photo is 3/4 x cm long and 20 cm wide than the width of the paper. The surface of the remaining paper surrounding the photograph is 990 cm2. Find the size of paper and photo.
  3. Rectangle
    squares2_3 Calculate area of the rectangle if its length is 12 cm longer than its width and length is equal to the square of its width.
  4. Rectangular land
    domcek On a rectangular land with dimensions of 35 m and 18.5 m is a house with a square floor plan with a side of 14 m. What % of the land is not occupied?
  5. Folded square
    square_folded ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD
  6. EQ2
    eq2_4 Solve quadratic equation: ?
  7. A rectangular patio
    rectangles A rectangular patio measures 20 ft by 30 ft. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.
  8. The length
    rectangle_14 The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.
  9. Two lands
    pozemky The common area of the two neighboring lands is 964 m2. The second land is 77 m2 smaller than twice the size of the first land. Find the areas of each land.
  10. Screens
    tv2_3 The area of a 25 inch TV screen is 300 inch² the area of a 40 inch TV screen is 768 inch². The area of the smaller screen is what percent of the area of the larger screen?
  11. Boxes
    krabice 200 boxes have been straightened in three rows. The first was 13 more than in the second, and in the second was one fifth more than in the third one. How many boxes are in each row?
  12. Trapezium
    trapezium_1 The area of trapezium is 35 cm2. Find its altitude if the bases are 6cm and 8 cm.
  13. Average height
    meter_22 The average height of all pupils is 162 cm. The class teacher's height is 178 cm. The average height of all (teacher and all pupils) is 163 cm. Calculate the number of pupils in the class.
  14. Fifth of the number
    numbs_5 The fifth of the number is by 24 less than that number. What is the number?
  15. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  16. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  17. Mean
    avg A student food the mean of 50 items as 38.6. When checking the work he found that he had taken one item as 50 why it should correctly read as 40 in this circumstances. What should be the correct mean?