The area of a square is the square of the length of one side. Define a function

Question

The area of a square is the square of the length of one side. Define a function f that expresses the area of a square as a function of its side length 8. syntax error: this is not an equation Use your function f to express that the area of a square is 81 square meters when the side length is 9 m. Write an expression using the function f that represents how much larger the area of a square with side length of 36 m is than the area of a square with side length of 23 m. Write an equation using f that represents the following statement: The total area of two squares, one with side length 7 m and the other with side length 11 m, is twice the area of a square which has a side length of y meters. Determine the value of y, the side length of the third square in part (d).

Explanation / Answer

a) let the side length of square = s

then area of square = s^2

hence the function becomes f(s) = s^2

b) when side length s = 9 cm

f(9) = 9^2 = 81

hence area = 81cm^2

c) let f(a) = a^2 and f(b) = b^2

f(a)-f(b) = a^2 - b^2

plugging a = 36 cm and b = 23 cm

f(a) - f(b) = 767 cm^2 larger than square of 23 cm

d) 7^2 + 11^2 = 2y^2

e) 49 + 121 = 2y^2

170 = 2y^2

y = 9.22 metres

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