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 result:

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

Solution:

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

$b_1=a_1+1=11+1=12\text{ m}$

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

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

$b_2=a_2+1=12+1=13\text{ m}$

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

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

$b_3=a_3+1=13+1=14\text{ m}$

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

$$\begin{gathered} S_3=y_3\cdot (a_3+b_3+c_3)=3\cdot (13+14+15)=126=126{\text{m}}^2 \\ \text{ Verifying Solution: } \\ {o}_1=2\cdot (y_1+a_1+b_1+c_1)=2\cdot (9+11+12+13)=90\text{ m } \\ {o}_2=2\cdot (y_2+a_2+b_2+c_2)=2\cdot (6+12+13+14)=90\text{ m } \\ {o}_3=2\cdot (y_3+a_3+b_3+c_3)=2\cdot (3+13+14+15)=90\text{ m} \end{gathered}$$

Try another example

Showing 0 comments:

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.
• 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.
• 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
• 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?
• 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?
• 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 rectangle with area 24 cm² a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
• Triangle - is RT?
  Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, side c is 31 cm longer than side a. Calculate the length of sides and determine whether triangle is a right triangle.
• 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.
• 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.
• 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 . .. .
• Rectangle - sides ratio
  Calculate the area of a rectangle whose sides are in ratio 3:13 and perimeter is 673.
• Rectangular field
  A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
• Land
  Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land?