Question

A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?
A. 46
B. 81
C. 126
D. 252

Answer 1

Hint: We draw a rough figure for the rectangular parking space and assume the dimensions of parking space as \[l \times b\] where ‘l’ is the length and ‘b’ is the breadth. Write an equation using the lengths of painted sides and write their sum equal to 37 feet.
* Area of a rectangle having length ‘l’ and breadth ‘b’ is given by the formula \[l \times b\]

Step-By-Step answer:
We have three sides of the rectangular parking space painted and one side is unpainted. Draw a diagram of rectangular parking space seen from above.

Here let us take three painted sides along with AB, BC and CD sides of the rectangle and the unpainted side is along with side AD.
We are given length of unpainted side is 9 feet
\[ \Rightarrow l = 9\] … (1)
Now we are also given sum of the lengths of the painted sides is 37 feet
\[ \Rightarrow l + b + b = 37\]
\[ \Rightarrow l + 2b = 37\]
Substitute the value of ‘l’ from equation (1)
\[ \Rightarrow 9 + 2b = 37\]
Shift all constants to RHS of the equation
\[ \Rightarrow 2b = 37 - 9\]
\[ \Rightarrow 2b = 28\]
Cancel same factors from both sides of the equation i.e. 2
\[ \Rightarrow b = 14\] … (2)
Then we can calculate area of parking space using the formula \[l \times b\]
Substitute the values of length and breadth from equations (1) and (2) in the formula
\[ \Rightarrow \]Area of parking space \[ = 9 \times 14\] square feet
\[ \Rightarrow \]Area of parking space \[ = 126\] square feet

\[\therefore \]Option C is correct.

Note: Many students make mistake of taking the lengths of the painted walls of the parking space as the same be it length or breadth and end up writing 3l or 3b, keep in mind the parking space forms a rectangle and we know opposite sides of rectangle are equal and parallel.