5 LB CHAP 29. NO- 11

[anik1989]

HELLO TOMMY, I THINK THE ANSWER SHOULD BE 1/2. WOULD YOU PLEASE CHECK THIS OUT?

DIagnol of small square, xroot2 = 7
so area of the small square x^2 = 49/2

area of the large square= 49

so shaded region =49- 49/2 = 49/2

so fraction of shaded region = '49/2/49=1/2

what do you say?

[danc]

I'm not an instructor but this is how I'd solve it.

What you can deduce from the information given is that the shaded triangles are all 3-4-5 triples. Why? Because the side of the big square that is 7 inches is divided into segments of 3 and 4, and, because the inscribed shape is a square, the corners of that square must divide the sides of the larger square in the same proportions. That is, each side of the larger square must be divided into segments of 3 and 4 by the corners of the inscribed square. As such, you know the sides of each triangle are 3 and 4. Therefore, the hypotenuse must be 5.

The hypotenuse of the triangle is the side of the smaller square, so the area of the smaller square is 5*5=25. Area of the larger square is 49, so to find the shaded area, you have to subtract the area of the smaller square from that of the larger square, 49-25=24. Therefore, the "fraction of the larger square" that is shaded is 24/49.

[tommywallach]

Hey Anik,

For what it's worth, I think you're assuming the smaller square's diagonal lines up with the sides, so it's also 7. But actually, the fact that the smaller square isn't perfectly placed in the middle of the larger square is obvious from the fact that the sides have been split UNEVENLY (3 on top and 4 on bottom, as opposed to 3.5 on top and bottom). This means that the diagonal of the square is not a straight up and down line, so it doesn't line up with the sides, so it must be LONGER than 7, as opposed to EQUAL to 7.

Hope that helps!

-t