Harry

Harry Thomson bought a large land in the shape of a rectangle with a circumference of 90 meters. He divided it into three rectangular plots. The shorter side has all three plots of equal length, their longer sides are three consecutive natural numbers. Find out the dimensions of each plot and the area of the whole plot.

Correct answer:

a₁ =  11 m
b₁ =  12 m
c₁ =  13 m
y₁ =  9 m
S₁ =  324 m²
a₂ =  12 m
b₂ =  13 m
c₂ =  14 m
y₂ =  6 m
S₂ =  234 m²
a₃ =  13 m
b₃ =  14 m
c₃ =  15 m
y₃ =  3 m
S₃ =  126 m²

Step-by-step explanation:

$$\begin{gathered} o=90\text{ m } \\ o=2y+2\cdot (a+b+c) \\ o=2y+2\cdot (a+a+1+a+2) \\ o=2y+2\cdot (3a+3) \\ 90=2\cdot y+6\cdot (a+1) \\ a>0,y>0,a>y \\ {a}_1=11;y_1=9=11\text{ m } \\ {a}_2=12;y_2=6 \\ {a}_3=13;y_3=3 \end{gathered}$$

$c_1=a_1+2=11+2=13\text{ m}$

$S_1=y_1\cdot (a_1+b_1+c_1)=9\cdot (11+12+13)=324{\text{m}}^2$

$c_2=a_2+2=12+2=14\text{ m}$

$S_2=y_2\cdot (a_2+b_2+c_2)=6\cdot (12+13+14)=234{\text{m}}^2$

$c_3=a_3+2=13+2=15\text{ m}$

Try another example

Related math problems and questions:

• Rectangles
  The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
• Rectangular garden
  The perimeter of Peter's rectangular garden is 98 meters. The width of the garden is 60% shorter than its length. Find the dimensions of the rectangular garden in meters. Find the garden area in square meters.
• The land
  The land, which has dimensions of 220 m and 308 m, the owner wants to divide into equally large square plots with the largest possible area. How long will one side of the plot be?
• Two rectangles
  I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm². What dimensions can this large rectangle have? Write all options. Explain your calc
• Rectangular plot
  The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the perimeter of the plot is 36m. Find the area of the diagonal of the plot.
• Interesting property
  Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle?
• Rectangle - sides
  What is the perimeter of a rectangle with area 266 cm² if length of the shorter side is 5 cm shorter than the length of the longer side?
• Land boundary
  The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary?
• Three gardens
  Is it possible to divide a plot of land with an area of 920 m² into three gardens in a ratio of 4: 2: 3 so that their areas are only whole multiples of square meters?
• Tiles
  The tile has the shape of a square with a side of 15 cm. What dimensions can a rectangle composed of 90 of these tiles have so that no tile remains?
• Triangle - is RT?
  Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, and side c is 31 cm longer than side a. Calculate the length of sides and determine whether a triangle is a right triangle.
• Rectangle
  The perimeter of the rectangle is 22 cm and content area 30 cm². Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
• Rectangle diagonals
  It is given a rectangle with an area of 24 cm² a circumference of 20 cm. The length of one side is 2 cm larger than the length of the second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
• Rectangular land
  Due to the new road, the longer dimension of the rectangular plot had to be shortened by 4 percent and the shorter dimension shortened by 10 percent. By how many percent has the area of land decreased?
• Three sides
  Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. .
• Rectangular garden
  The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
• Rectangle - area, perimeter
  The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.