anik89 wrote:

In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?( picture is on the attachment)

(A) 3/12

(B) 24/49

(C) 1/2

(D) 25/49

(E) 7/12

The first thing we need to recognize is that the 4 SHADED triangles are

identical. Here's why:

If we focus on one triangle and let

x and

y represent the 2 angles that are not 90 degrees, we get the following:

From this, we can see that

x +

y + 90° = 180°

So, when we examine another right triangle (this time in green)....

...we can see that the angle represented by

? must be equal to

x, since we already know that

x +

y + 90° = 180°

So, we'll add that information to the diagram...

Using similar logic, we can see that the 3rd angle in the green triangle must be equal to

y, since we know that

x +

y + 90° = 180°

Using the exact same process, we can show that all 4 shaded triangles have the same 3 angles:

x,

y and 90°

We're told that the white quadrilateral in the middle of the diagram is a SQUARE, so we can see that the hypotenuse in each of the SHADED triangles has the

same length.

This means that all 4 SHADED triangles are

identical....

So, the area of each SHADED triangle = (base)(height)/2 = (4)(3)/2 =12/2 = 6

So, the TOTAL area of all 4 SHADED triangles = (4)(6) = 24

The area of the LARGER square = (7)(7) = 49

So, 24/49 of the larger square is shaded

Answer:

Cheers,

Brent

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