Question

A builder wants to increase the size of one of his square patios. The patio measures 16 feet on each side. The builder plans to increase each side of the patio to be 125% of its current measure.

How many square feet larger is the area of the new patio than the area of the current patio?

Answer 1

144 square feet

Explanation:

The new dimension of the patio is the product of the original dimension and the scale factor. The builder's plans say the new dimension is 125% of the current dimension, so the new side length is ...

125% × 16 ft = 1.25 × 16 ft = 20 ft

The new patio area is (20 ft)² = 400 ft².

The original patio area is (16 ft)² = 256 ft².

The new patio is 400 -256 = 144 square feet larger than the current patio.

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Additional comment

Words like "increase", "larger", "more" and similar can suggest either addition of an amount, or multiplication by a factor. The problem statement must be parsed carefully in order to determine exactly what is meant. There can be some ambiguity when "larger" and "times larger" are used with percentages. (That is not the case here.)

The word "of" almost always means "times" in this context. So "125% of its current measure" means "125% times the current measure." Multiplication by the factor 1.25 is rightly described as an increase.

Answer 2

Explanation:

so, the area of an original patio is

16×16 = 256 ft²

now, when a side is increased to 125% of its original length, it means the original length is multiplied by 1.25

because the area calculation multiplies 2 sides, that increase factor is introduced twice into this multiplication.

so, it squares regarding the total area.

in other words

area new = 16×1.25 × 16×1.25 = 16² × 1.25² =

= area old × 1.25² = area old × 1.5625 =

= 400 ft²

the new patio area is therefore 400-256 = 144 ft² larger.