Question

Model the following problem with a quadratic equation. Then solve.Find the length of a side of a square with an area of 50 ft?.

Answer 1

The formula for determining the area of a square is expressed as

Area = length^2

Given that length = x and area = 50, it means that

50 = x^2

The standard form of a quadratic equation is expressed as

ax^2 + bx + c = 0

By modelling our equation, we have

x^2 - 50 = 0

It can also be written as

x^2 + 0x - 50 = 0

The general formula for solving quadratic equations is expressed as

`\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2-4ac}\text{ }}{2a} \\ a\text{ = 1, b = 0, c = - 50. thus} \\ x\text{ = }\frac{-\text{ 0 }\pm\sqrt[]{}0^2-4*1*-50}{2*1} \\ x\text{ =}\pm\text{ }\frac{\sqrt[]{200}}{2} \\ x\text{ = }(14.14)/(2)\text{ or x = }\frac{-\text{ 14.14}}{2} \\ x\text{ = 7.07 or x = - 7.07} \end{gathered}`

The length cannot be negative. Thus,

length = 7.07 ft