Question

A rectangle is formed from a square by adding 6 m to one side and 3 m to the other side. The area of the rectangle is 238 m². Find the dimensions of the original square.

Answer 1

Answer:

Therefore,

Dimensions of the Original Square is

$x =11\ m$

Step-by-step explanation:

Given:

Let the side of Square be "x" meter

Then the Dimensions of a Rectangle is formed by adding 6 m to one side and 3 m to the other side wil be.

$Length = x+6\\\\Width=x+3$

Area of Rectangle =238 m²

To Find:

x = ?  (Dimension of Original Square)

Solution:

Area of Rectangle is given by

$\textrm{Area of Rectangle}=Length\times Width$

Substituting the values we get

$238=(x+6)\times (x+3)$

Opening the Parenthesis we get

$238=x^{2}+9x+18\\\\x^{2}+9x+-220=0$    ......Which is Quadratic equation

On Factorizing and Splitting the middle term we get

$x^{2}+20x-11x-220=0\\\\x(x+20)-11(x+20)=0\\\\(x+20)(x-11)=0\\\\x+20=0\ or\ x-11=0\\\\x=-20\ or\ x=11$

As distance cannot be negative therefore,

$x =11$

Therefore,

Dimensions of the Original Square is

$x =11\ m$

Answer 2

Answer:

11 meter

Step-by-step explanation:

Given: A rectangle is formed from a square by adding 6 m to one side and 3 m to the other side.

The area of the rectangle is 238 m².

Now, finding the dimension of the original square.

Lets assume the side of square be "s".

∴ Width= $s+6$

Length= $s+3$

We know, area of rectangle= $width\times length$

Subtituting the value in the formula to find the dimension or side of square.

⇒

using distributive property of multiplication.

⇒$238= s^{2} + 3s+6s+18$

Subtracting both side by 238

⇒ $s^{2} + 9s-220= 0$

Solving by using quadratic formula to find value of s.

Formula: $\frac{-b\pm \sqrt{b^{2}-4(ac) } }{2a}$

∴ In the expression $s^{2} +9s-220$, we have a= 1, b= 9 and c= -220.

Now, subtituting the value in the formula.

= $\frac{-9\pm \sqrt{9^{2}-4(1\times-220) } }{2\times1}$

= $\frac{-9\pm \sqrt{81-4(-220) } }{2}$

= $\frac{-9\pm \sqrt{81+880 } }{2}$

= $\frac{-9\pm 31 }{2}$

= $\frac{-40}{2} or\ \frac{22}{2}$

= -20 or 11

Ignoring negative result as dimension cannot be negative.

∴ The dimension of square will be 11 meter.