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?

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126

252

answer is C.

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Detailed Solution

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. seo

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
⇒l=9… (1)
Now we are also given sum of the lengths of the painted sides is 37 feet
⇒l+b+b=37
⇒l+2b=37
Substitute the value of ‘l’ from equation (1)
⇒9+2b=37
Shift all constants to RHS of the equation
⇒2b=37−9
⇒2b=28
Cancel same factors from both sides of the equation i.e. 2
⇒b=14 … (2)
Then we can calculate area of parking space using the formula l×b
Substitute the values of length and breadth from equations (1) and (2) in the formula
⇒Area of parking space =9×14 square feet
⇒Area of parking space =126 square feet
∴ Option 3 is correct.

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