Continue the following pattern; describe the tenth figure in this pattern: 1 square, 4 squares in a 2 by 2 pattern, 9 squares in a 3 by 3 pattern, 16 squares in a 4 by 4 pattern. a. 81 small squares forming a larger 9 by 9 square b. 100 small squares forming a larger 10 by 10 square c. 100 small squares forming a larger 9 by 9 square d. 81 small squares forming a larger 10 by 10 square Please select the best answer from the choices provided A B C D

42 inches then 10 1/2 deep

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step-by-step explanation:

a

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240