# I hope you can give me any answer, Sana you can help me. Thank you Marvin owns a rectangular lot. The perimeter of the lot is 90m and its area is 450m2.a) What equation represents the perimeter of the lot? how about the equation that represents its area?b) How is given situation related to the lesson, sum and product of roots of quadratic equation?c) Using your idea of the sum and product of roots of quadratic equation, how would you determine the length and the width of rectangular lot?d) What are the dimension of the rectangular lot?

1
by Glai

2014-07-30T19:06:11+08:00
P = 2(l + w) = 90 => l + w = 45
A = lw = 450

We can consider l and w as the 2 roots of the quadratic equation.

(x - l)(x - w) = 0
x^2 - xl - xw + lw = 0
x^2 -x(l + w) + lw = 0
x^2 -45x + 450 = 0

then solve for x using the quadratic equation.

Another way to go through this is by substitution.
l + w = 45
l = 45 - w

lw = 450
(45 - w)(w) = 450
w^2 - 45w + 450 = 0

then solve for w and l using, again the quadratic equation.

it pretty much turned out the same huh

I'm the leaving the last question up to you. I'm sure you can do that :) Good luck