In the

In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm².

Correct result:

S =  160 cm²

Solution:

$$\begin{gathered} o=52\text{ cm } \\ o=2\cdot (a+b) \\ b\mathrm{/}2=3+a\mathrm{/}2 \\ 52=2\cdot (a+b) \\ b\mathrm{/}2=3+a\mathrm{/}2 \\ 2a+2b=52 \\ a-b=-6 \\ a=10 \\ b=16 \\ S=a\cdot b=10\cdot 16=160{\text{cm}}^2 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Rectangle
  The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm.
• The circumference
  The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
• Squares above sides
  Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm². The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc
• Two chords
  Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
• Rectangle
  Perimeter of rectangle is 48 cm. Calculate its dimensions if they are in the ratio 5:3 (width:height)
• Rhumbline
  Find circumference and area of the rhumbline ABCD if the short side AD of which has a length of 5 cm, and the heel of the height from D leading to the AB side divides the AB side into two sections of 3 cm and 4 cm.
• Rectangular trapezoid
  The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
• Trapezoid - intersection of diagonals
  In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate the trapezoid area.
• Ratio of sides
  Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
• Rectangle
  The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
• The bases
  The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
• 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.
• Four circles
  1) Calculate the circle radius if its area is 400 cm square 2) Calculate the radius of the circle whose circumference is 400 cm. 3) Calculate circle circumference if its area is 400 cm square 4) Calculate the circle's area if perimeter 400 cm.
• Rectangle - sides 3
  If in the rectangle ABCD we enlarge the side a by 5 cm and decrease the side b by 2 cm, the rectangle area will be reduced by 5 cm². When we decrease the length of the side a by 4 cm and and at the same time we increase the length of side b by 3 cm we inc
• Area to perimeter
  Calculate circle circumference if its area is 254.34cm2
• Trapezoid
  How long are the trapezoid bases with area 24 cm² and height 3 cm. One base is 3 times longer than the shorter.
• Rectangle - sides 4
  Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.