Mang juan owns a rectangular lot.The perimeter of the lot is 90m its area is 450m2. questio: 1.what equation represent the perimeter of the lot? how about the equation that represents its area? 2.how is the given situation related to the lesson ,the sum and the product of roots of quadratic equation 3.using your idea of sum and product of roots of quadratic equation ,how would you represent the length and the width of the rectangular lot? 4.what are the dimensions of the rectangular lot?

2

Answers

2014-09-28T21:14:15+08:00
Let 'x' be one side of the rectangular lot
     'y' be the other side
Perimeter:
   P = 2x + 2y
   2x + 2y = 90
Area:
   A = xy
   xy = 450

Since the product of the roots is defined by:
x1 × x2 =  \frac{C}{A}
and sum of the roots is
x1 + x2 = - \frac{B}{A}
where A is the coefficient for x², B for x and C is the constant.
Using the equations above, we will know that the product of the roots or in that case is the dimensions of the lot is represented by the equations:
2x + 2y  = 90 and xy = 450
or reducing the first equation to lowest term by dividing the whole equation by '2' we'll have x + y = 45
dividing the sum and product of the roots, we'll have
 \frac{ \frac{-B}{A} }{ \frac{C}{A} }  =  \frac{45}{450}
 \frac{-B}{C} =  \frac{45}{450}
So we'll have B = -45 and C = 450
Considering the equation we'll have:
Ax² + Bx + C = 0
then we'll divide the equation with A since we don't know its coefficient:
x^{2} -  \frac{45}{A} + \frac{450}{A} = 0
 x^{2} - 45x + 450 = 0
solving for x:
x = 30 and 15
and those are already the dimensions..
Since the standard is that the length is of bigger value than that of the width then considering that common knowledge, you'll have length as 30 and width as 15
5 4 5
where did you get 2x and 2y ?
from the formula of perimeter
it is stated on the 4th line of the solution
tnx ate
you're welcome
2014-09-28T21:54:27+08:00
Let x be one side of the rectangular lot
     y be the other side
Perimeter:
   P = 2x + 2y
   2x + 2y = 90
Area:
   A = xy
   xy = 450

Since the product of the roots is defined by:
x1 × x2 = 
and sum of the roots is

where A is the coefficient for x², B for x and C is the constant.
Using the equations above, we will know that the product of the roots or in that case is the dimensions of the lot is represented by the equations:
2x + 2y  = 90 and xy = 450
or reducing the first equation to lowest term by dividing the whole equation by '2' we'll have x + y = 45
dividing the sum and product of the roots, we'll have


So we'll have B = -45 and C = 450
Considering the equation we'll have:
Ax² + Bx + C = 0
then we'll divide the equation with A since we don't know its coefficient:


solving for x:
x= 30 and 15
and those are already the dimensions..
Since the standard is that the length is of bigger value than that of the width then considering that common knowledge, you'll have length as 30 and width as 15.
1 5 1