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In the 7-inch square above, another square is inscribed. What fraction

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In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

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New post 11 Oct 2018, 02:00
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In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?


(A) \(\frac{3}{12}\)

(B) \(\frac{24}{49}\)

(C) \(\frac{1}{2}\)

(D) \(\frac{25}{49}\)

(E) \(\frac{7}{12}\)


Attachment:
Capture (2).JPG
Capture (2).JPG [ 15.52 KiB | Viewed 527 times ]

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Re: In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

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New post 11 Oct 2018, 19:05
Bunuel wrote:
Image
In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?


(A) \(\frac{3}{12}\)

(B) \(\frac{24}{49}\)

(C) \(\frac{1}{2}\)

(D) \(\frac{25}{49}\)

(E) \(\frac{7}{12}\)


Attachment:
The attachment Capture (2).JPG is no longer available


So every corner makes a right angled triangle with sides 3-4-5...
And hypotenuse of this triangle is the side of inner square, so 5..

Area of shaded region = \(7^2-5^2=49-25=24\)
Total area =7^2=49

Shaded region as a fraction of total =\(\frac{24}{49}\)

B
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Re: In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

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New post 13 Oct 2018, 17:50
Bunuel wrote:
Image
In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?


(A) \(\frac{3}{12}\)

(B) \(\frac{24}{49}\)

(C) \(\frac{1}{2}\)

(D) \(\frac{25}{49}\)

(E) \(\frac{7}{12}\)


Attachment:
Capture (2).JPG


The area of the larger square is 7^2 = 49. We see that each of the shaded regions is a right triangle that is a 3-4-5 right triangle. Thus, each of these right triangles has an area of ½ x 3 x 4 = 6, and the total area of the four triangles is 6 x 4 = 24. So the fraction of the larger square is shaded is 24/49.

Answer: B
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Re: In the 7-inch square above, another square is inscribed. What fraction   [#permalink] 13 Oct 2018, 17:50
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