Question

What is the area of a rectangle that has a length of $5x+3$ and width of $ 2x-3$?

Answer 1

Hint: We are given the length and breadth of the rectangle in terms of a variable. We know the area of the rectangle is simply the length multiplied by the breadth, so we need to do some variable algebra here. Note here that the area will be calculated in terms of variable only.

Complete step by step solution:
We are given the length of $5x+3$ and the breadth of $2x-3$. We know that if the length of a rectangle is ‘l’ and the breadth of the rectangle is ‘b’ then the area of the rectangle is given by $a\times b$. We have the following formula:
Area of rectangle=Length of rectangle $\times$ Breadth of rectangle
Keeping this in mind, we assume that the area is ‘A’, then putting the value of ‘l’ and ‘b’ as given in the question, we have:
$A=(5x+3)\times(2x-3)$
Multiplying the first term 5x by 2x we have $5x\times2x=10x^2$.
Next we multiply 5x by $-3$, so we have $5x\times-3=-15x$.
After this we multiply $3$ by 2x, we get $3\times 2x=6x$.
Finally, we multiply $3$ by $-3$, and we have $3\times -3=-9$.
Putting these terms together, we get the required area of the rectangle.
$A=10x^2-15x+6x-9$
Now collecting the terms of the variable ‘x’, we simplify the expression further to obtain the following:
$A=10x^2-9x-9$
Hence, the area is calculated.

Note: Do not do any calculation mistake while collecting the terms in the variables. You have to multiply length and breadth, do NOT add them. Remembering the formulae of areas is very important, since such questions are asked frequently.