If in the figure above, semicircles X and Y have radii of 6 and 8 feet, respectively, then what is the area of semicircle Z (in square feet)? (Note: Figure not drawn to scale.) A. 10π B. 20π C. 25π D. 50π E. 100π

(D) If the radii of the semicircles X and Y are 6 feet and 8 feet, then their diameters are 12 and 16 feet. These diameters are both lengths of the legs of a right triangle, and the diameter of semicircle Z is the hypotenuse of this triangle.

The triangle is a 3-4-5 triangle, since the perpendicular legs are in the ratio 3 : 4. So the hypotenuse measures 20 feet, meaning the diameter of Z is 20 feet and its radius is 10 feet.

To determine the area of semicircle Z, we will determine the area of a full circle with the same radius as Z, and then divide this quantity by 2.

The area of a circle with radius 10 is: Area = πr² Area = π10² = 100π.

Thus, the area of semicircle Z is 50π square feet. The correct answer is choice (D). ----------

If the triangle is a 3:4:5,then shouldn't the legs of the triangle be 12, 16 and 25? The hypotenuse shouldn't be 20, it should be 25, correct? This means the radius is 25/2.

If the triangle is a 3:4:5,then shouldn't the legs of the triangle be 12, 16 and 25?

No, your reasoning is NOT correct.

The 12 : 16 : 25 triangle is a 3 : 4 : 25/4, but NOT a 3 : 4 : 5 triangle. You can also check, that 25² = 625, while 12² + 16² = 144 + 256 = 400 = 20².

So note, that a 3:4:5 triangle is a triangle, which sides result in a 3:4:5 proportion, which is the same as 3a : 4a : 5a.

Users browsing this forum: No registered users and 2 guests

You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum

GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.