The area of a square mat is 125 square inches. The best approximation of its length is inches. If the length of each side is increased by another inch, the area would increase by approximately square inches.

The area of a square is simply the side length squared and we are given that the area is 125 so:

s^2=125

s=√125

s=5√5

Now using the area equation again, and adding 1 inch to s we have:

A=(s+1)^2, and using s found above we have:

A=(5√5+1)^2

A=125+10√5+1

A=126+10√5 in^2

A≈148.36 in^2 (to nearest hundredth of a square inch)

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akposevictor akposevictor · Answer 2 · 2022-02-04T12:25:58+01:00

The area of the square increased by approximately 23.84 sq. in.

Area of a Square

Area of a square, where s is the side length, given that all it's four sides are always equal, can be determined using the formula, A = s².

Given:

Area of square (A) = 125 sq. in.

Therefore:

s = √125 = 11.2 in.

Length of the square = 11.2 in.

Increasing the length by another inch, we would have new length = 11.2 + 1 = 12.2 in.

New Area of square = 12.2² = 148.84 sq. in.

The difference between both areas = 148.84 - 125 = 23.84 sq. in.

Therefore, the area of the square increased by approximately 23.84 sq. in.

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