The area of a rectangular pool is 1260ft^2. Find the dimensions of the pool given that one side is 48ft longer than 3 times the other.

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Ответ:

xxaurorabluexx

02.12.2020

Mathematics

60 feet

Step-by-step explanation:

The area of the school is

165(300) = 49500 square feet.

The area of the parking lot with the school is

(165+75)(300+75) = 240(375) = 90000 square feet. This means the area of just the parking lot is

90000-49500 = 40500 square feet.

The area of the new expanded lot will be doubled; this means it will be

2(40500) = 81000 square feet. Adding back the area of the school, this means the total lot will be

81000+49500 = 130500 square feet.

The width will be 375+x and the length will be 240+x; this gives us

130500 = (375+x)(240+x)

Multiplying the binomials gives us

130500 = 90000+375x+240x+x²

130500 = 90000+615x+x²

To solve this, we first set it equal to 0. We do this by subtracting 130500 from each side:

130500-130500 = 90000+615x+x²-130500

0 = x²+615x-40500

We will use the quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substituting our values for a, b and c,

$x=\frac{-615\pm \sqrt{615^2-4(1)(-40500)}}{2(1)}\\\\=\frac{-615\pm \sqrt{378225--162000}}{2}\\\\=\frac{-615\pm \sqrt{378225+162000}}{2}\\\\=\frac{-615\pm \sqrt{540225}}{2}\\\\=\frac{-615\pm 735}{2}\\\\=\frac{-615+735}{2}\text{ or }\frac{-615-735}{2}\\\\=\frac{120}{2}\text{ or }\frac{-1350}{2}\\\\=60\text{ or }-675$

We do not use negative numbers for measurement, so x = 60.

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