Complete the stemplot for the following data. 33 46 23 38 33 31 52 20 20 22 34 30 44 28 33 39 33 37 58 32 43 35 26 24 30 22 57 4
1 answer:
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The length of the rectangle = 16 meters
The width of the rectangle = 10.5 meters
<u>Step-by-step explanation</u>:
Given that,
The Area of the rectangle is 273.
<u><em>Step 1</em></u><em> :</em>
Let, the width of the rectangle be 'x'
The length of the rectangle is 2x - 5
<u><em>Step 2</em></u><em> :</em>
Area of the rectangle = length width
273 = (2x - 5) x
273 = 2x^2 - 5x
<u><em>Step 3</em></u><em> :</em>
The equation formed is 2x^2 - 5x -273 = 0
a= coefficient of x^2 = 2
b= coefficient of x = -5
c = constant = -273
Find the roots of the equation, to find the width.
<u><em>Step 4</em></u><em> :</em>
Find the roots using factorizing method,
ac = 2-273 = -546 and b= -5
Factorizing -546 as -2621
The product of -2621 = -546
The sum of -26 + 21 = -5
<u><em>Step 5</em></u><em> :</em>
The roots of the equation 2x^2 - 5x -273 = 0 are x= -26/2 and x= 21/2
The values of x are x= -13 and x= 10.5
Since the width cannot be a negative value, neglect x= -13
<u><em>Step 6</em></u><em> :</em>
Therefore,
The width of the rectangle = 10.5 meters
The length of the rectangle = 2x-5
= 2(10.5) - 5
= 21 - 5
length = 16 meters