What is the scale factor of a house if 1/4 sq. Inch equals 5 sq. Feet (1sq. inch= 20sq. feet)?
If 1sq inch = 20sq feet
So, if I take a side of 1 inch in my model, it will correspond to √20.
Because 1 inch * 1 inch = 1 sq inch
And √20 feet * √20 feet = 20 sq feet
Scale factor = Larger length of segment/Smaller lenght
= √20 feet/1 inch
= √20*12 inches/ 1 inch
= √20*12
= 53.66
1/4 square inches -----> 5 square ft
1/2 inch -----> √5 ft
1 inch -----> 2√5 ft
1 inch ----- 2√5(12) = 24√5 inches
scale : 1 : 24√5 or appr 1 : 53.67 , just like Arora had.
To find the scale factor of a house, we need to compare the ratios of the areas in square inches and square feet. The ratio is given as 1/4 square inch equals 5 square feet.
Let's set up a proportion to find the scale factor. We know that 1 square inch is equivalent to 20 square feet, so we can write:
1/4 square inch = 5 square feet
1 square inch = 20 square feet
To find the scale factor, divide the square footage values on both sides of the equation:
(1/4 square inch) / (1 square inch) = (5 square feet) / (20 square feet)
Simplifying the equation:
1/4 = 5/20
Cross-multiplying:
20 = 4 * 5
20 = 20
Therefore, the scale factor of the house is 1. This means that the house retains its original proportion and size.