Question

The area of the rectangle exceeds the area of the square by 24 m². Find x.​

Answer 1

Answer:

The required value of $x$ is $\boxed{\bf x=6.2}$.

Step-by-step explanation:

Consider the length and breadth of the rectangle as $L$ and $B$ respectively.

The expression which represent the length of the rectangle is as follows:

$L=\left(x-3\right)\text{m}$

The expression which represent the breadth of the rectangle is as follows:

$B=\left(x-6\right)\text{m}$

The expression which represent the side of the square is as follows:

$\text{Side}=\left(x-7\right)$

Area of a rectangle is calculated as shown below:

$\boxed{\text{Area}=\text{Length}\times \text{Breadth}}$

To obtain the expression for the area of the rectangle substitute the expression of length and breadth is the above equation as shown below:

$\begin{aligned}\text{Area of rectangle}&=\left(x-6\right)\times \left(x-3\right)\\&=x^{2}-9x+18\end{aligned}$

The formula to calculate the area of a square is as follows:

$\boxed{\text{Area of square}=\left(\text{Side}\right)^{2}}$

Calculate the area of the square as shown below:

$\begin{aligned}\text{Area of square}&=\left(x-7\right)^{2}\\&=x^{2}-14x+49\end{aligned}$

It is given that the area of the rectangle is $24\text{m}^{2}$ greater than the area of the square.

The equation formed as per the above statement is as follows:

$\begin{aligned}\text{Area of rectangle}&=\text{Area of square}+24\\x^{2}-9x+18&=x^{2}-14x+49\\14x-9x&=49-18\\5x&=31\\x&=\dfrac{31}{5}\\x&=6.2\end{aligned}$

Therefore, the required value of $x$ is $\boxed{\bf x=6.2}$.

Answer 2

Answer:

x=11

Step-by-step explanation:

There is a rather easier way to solve this math.

We know that the formula for area of a square or rectangle = length * width

So first we are going to find their areas in terms of x.

Area of square in terms of x : (x-7)*(x-7)

(x-7)^2

Area of rectangle in terms of x : (x-3)(x-6)

Now, it is given in the question that the area of the rectangle exceeds the area of the square by 24m^2.We can write the whole thing in the form of an equation like this :

(x-3) (x-6)=(x-7)^2 + 24

x^2-6x-3x+18=x^2-14x+49+24

x^2 -9x+18=x^2 -14x+73

x^2 -x^2 -14x+9x+73-18=0

-5x=-55

x=11 (ans.)

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