Name: Application of Quadratic Equation
Uploaded: 2019-07-19
Duration: 7 min 46 s
Description: There are many real-world situations that deal with quadratic equations: calculating areas, determining a product's profit, formulating the speed of an objec...

Question

50 m

of fencing is used to make three sides of a rectangular area, using an existing wall as the fourth side. The area of the rectangle is

150 m^{2}

. Determine the dimensions of the rectangular area.

Accepted Answer

It is given that $50 m$ of fencing is used to make three sides of a rectangular area.

i.e. $2 (width) + length = 50$

$\Rightarrow Length = 50 - 2 (width) . . . (1)$

Let the width of the rectangular area be $x m$ .

Then, using $(1)$ length $= (50 - 2 x) m$

Also, it is given that area of rectangular area $= 150 m^{2}$

i.e. $(50 - 2 x) \times x = 150 [∵ Area = length \times width]$

$\Rightarrow - 2 x^{2} + 50 x = 150$

$\Rightarrow 2 x^{2} - 50 x + 150 = 0$

$\Rightarrow x^{2} - 25 x + 75 = 0$

Now, $x_{1, 2} = \frac{- (- 25) \pm \sqrt{(- 25)^{2} - 4 \cdot 1 \cdot 75}}{2 \cdot 1}$ [Using quadratic formula]

$\Rightarrow x_{1, 2} = \frac{25 \pm \sqrt{625 - 300}}{2}$

$\Rightarrow x_{1, 2} = \frac{25 \pm \sqrt{325}}{2}$

$\Rightarrow x_{1, 2} = \frac{25 \pm 5 \sqrt{13}}{2}$

$\Rightarrow x_{1} = \frac{25 + 5 \sqrt{13}}{2}, x_{2} = \frac{25 - 5 \sqrt{13}}{2}$

$\Rightarrow x_{1} = 21.5, x_{2} = 3.49$

When $x = 21.5$ , then length $= 50 - 2 (21.5) = 7$

When $x = 3.49$ , then length $= 50 - 2 (3.49) = 43.02$

Hence, the dimensions of the rectangular area are $3.49 m by 43.02 m or 21.5 m by 7 m$

$50 m$ of fencing is used to make three sides of a rectangular area, using an existing wall as the fourth side. The area of the rectangle is $150 m^{2}$ . Determine the dimensions of the rectangular area.

Important Questions on More than One Way to Solve a Problem (Equivalent Forms)

Learn and Prepare for any exam you want !

50 m of fencing is used to make three sides of a rectangular area, using an existing wall as the fourth side. The area of the rectangle is 150 m2. Determine the dimensions of the rectangular area.

Important Questions on More than One Way to Solve a Problem (Equivalent Forms)

Learn and Prepare for any exam you want !

$50 m$ of fencing is used to make three sides of a rectangular area, using an existing wall as the fourth side. The area of the rectangle is $150 m^{2}$ . Determine the dimensions of the rectangular area.