Question

Corners of equal size are cut from a square with sides of length 8 meters (see figure).
Determine the domain of the function. (Enter your answer using interval notation.)
(b) Use a graphing utility to graph the area function over its domain. Use the graph to find the range of the function. (Enter your answer using interval notation.)
What would be the length of each side s of the figure?

Answer 1

The domain of the function is given as -4√2 and 4√2

the length of the sides is 8cm

How to solve for the shape

The area of this square is given as 8 x 8 = 64

each shaded triangle is a right angled triangle

1/2 *x*x = x²/2

Since we have 4 triangles we would have

4x²/2

When the triangles are cut the area would be

A = 64 - 2x²

such that 64 = 2x²

x² = 32

domain would be x =  ± √32

-4√2 , 4√2

b. The solution to the graph is contained in the image that i have attached.

c. The length of each of the sides would be √64. Remember that this is a square.

Hence the length is = 8

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