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:

$ab = 266 \ \\ b = a + 5 \ \\ a(a+5) = 266 \ \\ a^2 + 5 a - 266 =0 \ \\ \ \\ a^2 +5a -266 =0 \ \\ \ \\ p=1; q=5; r=-266 \ \\ D = q^2 - 4pr = 5^2 - 4\cdot 1 \cdot (-266) = 1089 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ -5 \pm \sqrt{ 1089 } }{ 2 } \ \\ a_{1,2} = \dfrac{ -5 \pm 33 }{ 2 } \ \\ a_{1,2} = -2.5 \pm 16.5 \ \\ a_{1} = 14 \ \\ a_{2} = -19 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -14) (a +19) = 0 \ \\ \ \\ \ \\ a = 14 \ \\ b= 19 \ \\ o = 2(a+b) = 66 \ \text{cm}$

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

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:

Next similar math problems:

• Rectangles - sides
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?
• Rectangle vs square
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.
• 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 . .. .
• 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?
• Two bodies
The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco
• 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
• 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.
• Rectangle SS
Perimeter of a rectangle is 268 cm and its diagonal is 99.3 cm. Determine the dimensions of the rectangle.
• Rectangle
There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
• 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.
• 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.
• Do you solve this?
Determine area S of rectangle and length of its sides if its perimeter is 102 cm.
• Rectangle
The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
• Isosceles triangle 9
Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm, and the altitude is 24cm. Find the area of the isosceles triangle.
• Playground
The land for the construction of the school playground has the shape of a rectangle with a shorter side of 370 m. Its other side is 260 m longer. How many meters of the fence does the school need to buy on the fencing playground?
• Trapezoid 15
Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4