Question

On a house blueprint, 2 feet is represented by 1 inch. If a room on the blueprint measures 5 inches by 6 inches, what is the area of the actual room?
a) 30 square feet
b) 60 square feet
c) 90 square feet
d) 120 square feet

Answer 1

Hint: convert the length and breadth of the given room on the blueprint to the actual dimensions with the help of the units defined in question i.e. 1 inch on blueprint = 2 feet original. Now, find the area of the room with the help of the relation given as
$\text{Area of rectangle}=\text{length}\times \text{breadth}$

Complete step-by-step answer:
As it is given that 1 inch on the blueprint of the house will actually represent 2 feet in reality and hence, we need to determine the area of the actual room if the length and breadth of the room on the blueprint are 5 inches and 6 inches.
So we are representing 2 feet by 1 inch in the blueprint, hence we need to convert the dimensions of the room given in inches to feet for calculating the actual area. So, we have dimensions of room as length = 5 inches, breadth = 6 inches.
As 1 inch length on blueprint = 2 feet in real. Hence, 5 inch (length of room) on blueprint is
$5\times 2$ feet in real = 10 feet
Similarly, 6 inches (breadth) on blue print $=6\times 2=12$ feet in real.
Hence, the actual dimension of the room is 10 feet by 12 feet. As we know the geometrical shape of a room is a rectangle. So, we need to use identity for calculating area of rectangle which can be given as
$\text{Area of rectangle}=\text{length}\times \text{breadth}$
Hence, area of the actual room $=10\times 12=120$ square feet
So, option (d) is the correct answer.

Note: Another approach for the question would be that we can get area of the room on blueprint in $inche{{s}^{2}}$ and hence convert it to $\text{fee}{{\text{t}}^{2}}$ by multiplying by $2\text{feet}\times 2\text{feet}$ as we have
1 inch = 2 feet
$1\text{inc}{{\text{h}}^{2}}=4\text{fee}{{\text{t}}^{2}}$
So, multiplying the area on blueprint by 4 to get the answer. One may be wrong by the above approach if he or she multiplied the area in $inche{{s}^{2}}$ by 2 feet only. So, he or she will get the wrong answer. Hence, we need to take care if going through the above solution. Don’t use any other conversions in real life. Use the given conversion criteria to solve the given question.