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Question
please sir,solve this:the area of a rectangular floor is 13.5m^2 one side is 1.5m longer than the other.
(a)calculate the dimensions of the floor.
(b)if it costs #250.00 per square metre to carpet the floor and only #2,200.00 is available, what area of the floor can be covered with carpet?

Answer
(a)

Area of rectangle = length (x) * breadth (y) ..................(1)
One side is 1.5 m longer than the other.
Hence
x = y +1.5 ......................(2)

Area = 13.5 (given)

Hence, from equation (1) and (2) above,
Area = (y+1.5)*y
13.5 = y^2 + 1.5y
Rearranging,

y^2+1.5y-13.5=0  ................. (3)

This is a quadratic equation, where a=1, b=1.5, c=-13.5

Hence roots of this equation are,

y = (-b+/-Sqrt(b^2-4ac)/2a
y = (-1.5 +/- Sqrt (2.25-4*(-13.5))/2
y = (-1.5 +/- Sqrt (2.25+54))/2
y = (-1.5 +/- 7.5)/2
y = 6/2 or y = -9/2
y=3 OR y = -4.5

However breadth cannot be negative.
Hence y = 3 .................(4)

Putting this in equation 2, we get,
x = 4.5 ...........(5)

Hence length of the rectangle is 4.5 m and breadth is 3.

NOTE: For part (a), you need understanding of quadratic equations. If you are not aware of it, then please visit

http://www.wikihow.com/Find-the-Roots-of-a-Quadratic-Equation

This webpage explains how to find roots of quadratic equation. I have not repeated it here to avoid duplication and copy.

(b)
Since per sq mtr cost is $250, we can cover total (2200/250) = 8.8 sq mtr in the available budget of $2200.


I hope this helps.
All the best!

Pawan  

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Pawan Musale

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I can answer questions wrapped in words. This includes questions related to Logic, Natural Numbers, Integers, Real Numbers, Complex Numbers, Number Theory, Geometry, Trigonometry, Graph Theory, Square Roots, Basic Integration, Profit-Loss problems, Work-Time problems, Equations etc.

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Tutoring on www.allexperts.com since long time.

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I am Bachelor of Engineering from the reputed institute in India.

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