Math Question

[ATX04UT]

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Can anyone help me with these problems?

1. When each of the sides of a square is increased by one yard, the area of the new square is 53 square yards more than that of the original square. What is the length of the sides of the original square?

Answer: 26

2. What is the maximum number of 3 inch squares (squares that are 3 inches on a side) that can be cut from a sheet of tin 19 x 23 inches?

Answer: 42

I can't figure these out!!!!!!!!!!!!!!! please help, hints, anything.....
Thanks!!!
🙂

 

[bluekty]

Q1.
(x+1)^2 = 53 + x^2
x^2 + 2x +1 = 53 + x^2
2x + 1 = 53
2x = 52
x = 26

Q2.
one the side 23": there could be 7 of 3" (7*3 = 21 :shouldn't go over 23")
one the side of 19": 6 of 3" can fit in (6*3 = 18 which doesn't go over 19")
Therefore, 6*7 = 42 of 3" square can fit in.

 

[ATX04UT]

Q1.
(x+1)^2 = 53 + x^2
x^2 + 2x +1 = 53 + x^2
2x + 1 = 53
2x = 52
x = 26

Q2.
one the side 23": there could be 7 of 3" (7*3 = 21 :shouldn't go over 23")
one the side of 19": 6 of 3" can fit in (6*3 = 18 which doesn't go over 19")
Therefore, 6*7 = 42 of 3" square can fit in.

THANK YOU!