Re: In the 7-inch square above, another square is inscribed. Wha
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15 Nov 2018, 00:48
This problem seems more intuitive to me, so I'll do my best to explain it.
The problem starts off by saying that this is a 7-inch square and we need to find the fraction that is shaded. Since this is implying area without saying it, we can multiply both sides to get a total area of 49 for the big square.
To get the smaller square, it is a little harder for me to explain. In the sides, we see that there is a 3 and 4. Because a square is even on all the sides, you can put a 4 at the top bordering the 3 or a 3 on the bottom bordering the 4. From here we realize that both sides are now 3 and 4, which fit into Pythagorean's Theorem of a 3,4,5 area triangle. The hypotenuse of 5, would be a side of the inner triangle. This is important because we can now find the inner square.
If the inner square is 5-inches, it means it covers a total of 25 square inches.
From the original 7-inch square, we see that it is 49 inches. So, 49-25 = 24 inches left unshaded, out of the 49 possible, hence the fraction \frac{24}{49}.
B is your answer.