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

A rectangular garden measures

24 m by 32 m

. A path of uniform width is built all around the outside of the garden. The total area of the path and the garden is

1540 m^{2}

. Find the width of the path.

Accepted Answer

It is given that rectangular garden $(A B C D)$ measures $24 m by 32 m$ .

Let the width of the path be $x m$ .

Then, the dimension $E F G H$ measures $(24 + 2 x) m by (32 + 2 x) m$

Also, it is given area of the path and garden $= 1540 m^{2}$ .

i.e. $(24 + 2 x) (32 + 2 x) = 1540$

$\Rightarrow (12 + x) (16 + x) = \frac{1540}{4}$

$\Rightarrow 192 + 12 x + 16 x + x^{2} = 385$

$\Rightarrow x^{2} + 28 x + 192 - 385 = 0$

$\Rightarrow x^{2} + 28 x - 193 = 0$

$\Rightarrow x_{1, 2} = \frac{- 28 \pm \sqrt{{(28)}^{2} - 4 \cdot 1 \cdot (- 193)}}{2 \cdot 1}$ [Using quadratic formula]

$\Rightarrow x_{1, 2} = \frac{- 28 \pm \sqrt{784 + 772}}{2}$

$\Rightarrow x_{1, 2} = \frac{- 28 \pm \sqrt{1556}}{2}$

$\Rightarrow x_{1, 2} = \frac{- 28 \pm 2 \sqrt{389}}{2}$

$\Rightarrow x_{1} = \frac{- 28 + 2 \sqrt{389}}{2}, x_{2} = \frac{- 28 - 2 \sqrt{389}}{2}$

$\Rightarrow x_{1} = 5.7, x_{2} = - 33.7$

Since, $x$ being length cannot be negative hence $x_{2} = - 33.7$ is not possible and only solution is $5.7 m$ .

So, the width of the path is $5.7 m$

A rectangular garden measures $24 m by 32 m$ . A path of uniform width is built all around the outside of the garden. The total area of the path and the garden is $1540 m^{2}$ . Find the width of the path.

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

Learn and Prepare for any exam you want !

A rectangular garden measures 24 m by 32 m. A path of uniform width is built all around the outside of the garden. The total area of the path and the garden is 1540 m2. Find the width of the path.

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

Learn and Prepare for any exam you want !

A rectangular garden measures $24 m by 32 m$ . A path of uniform width is built all around the outside of the garden. The total area of the path and the garden is $1540 m^{2}$ . Find the width of the path.