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?

Correct result:

x =  66 cm

Solution:

ab=266 b=a+5 a(a+5)=266 a2+5a266=0  a2+5a266=0  p=1;q=5;r=266 D=q24pr=5241(266)=1089 D>0  a1,2=q±D2p=5±10892 a1,2=5±332 a1,2=2.5±16.5 a1=14 a2=19   Factored form of the equation:  (a14)(a+19)=0   a=14 b=19 o=2(a+b)=66 cmab = 266 \ \\ b = a + 5 \ \\ a(a+5) = 266 \ \\ a^2 + 5 a - 266 =0 \ \\ \ \\ a^2 +5a -266 =0 \ \\ \ \\ p=1; q=5; r=-266 \ \\ D = q^2 - 4pr = 5^2 - 4\cdot 1 \cdot (-266) = 1089 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ -5 \pm \sqrt{ 1089 } }{ 2 } \ \\ a_{1,2} = \dfrac{ -5 \pm 33 }{ 2 } \ \\ a_{1,2} = -2.5 \pm 16.5 \ \\ a_{1} = 14 \ \\ a_{2} = -19 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -14) (a +19) = 0 \ \\ \ \\ \ \\ a = 14 \ \\ b= 19 \ \\ o = 2(a+b) = 66 \ \text{cm}



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators

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:

  • Rectangle diagonals
    rectangle_diagonals_1 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.
  • Rectangles - sides
    rectangles_2 One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm2. What are the dimensions of the original rectangle?
  • Parallelogram
    quadrilateral_parallelogram The perimeter of the parallelogram is 417 cm. The length of one side is 1.7-times longer than the length of the shorter side. What is the length of sides of a parallelogram?
  • Rectangles
    rectangle_15 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?
  • The hall
    lucerna The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m2. What were the original dimensions of the hall?
  • Circle and rectangle
    described_circle A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.
  • The sides
    rectangle_9 The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
  • Diagonal 20
    plaza Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
  • Plot
    rectangle_5 The length of the rectangle is 8 smaller than three times the width. If we increase the width by 5% of the length and the length is reduced by 14% of the width, the circumference of rectangle will be increased by 30 m. What are the dimensions of the recta
  • Rectangle vs square
    squares One side of the rectangle is 1 cm shorter than the side of the square, the second side is 3 cm longer than the side of the square. Square and rectangle have the same content. Calculate the length of the sides of a square and a rectangle.
  • Ratio of sides
    described_circle2 Calculate the area of a circle that has 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
    diagonal In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
  • Rectangular garden
    rectangle_1 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.
  • Property
    pozemok The length of the rectangle-shaped property is 8 meters less than three times of the width. If we increase the width 5% of a length and lendth reduce by 14% of the width it will increase the property perimeter by 13 meters. How much will the property cost
  • The rectangle
    rectangles_6 Determine the area of the rectangle where the length and width are in the ratio 5:2 and its length is 7.5 cm longer than its width. Determine also its length and its width.
  • Square vs rectangle
    ctverec 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.
  • Rectangle
    diagonal_rectangle_2 The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.