aljatar wrote:
A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?
A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800
ALWAYS LOOK FOR SPECIAL TRIANGLES.
Draw the rectangle and its diagonal:
Attachment:
diagonal_of_200.png [ 4.63 KiB | Viewed 21094 times ]
Since diagonal AD is a multiple of 5 -- and every value in the problem is an INTEGER -- check whether triangle ABD is a multiple of a 3:4:5 triangle.
If each side of a 3:4:5 triangle is multiplied by 40, we get:
(40*3):(40*4):(40*5) = 120:160:200
The following figure is implied:
Attachment:
diagonal_of_200_1 (1).png [ 5.86 KiB | Viewed 21086 times ]
Check whether the resulting perimeter for rectangle ABCD is 560:
120+160+120+160 = 560
Success!
Implication:
For the perimeter of rectangle ABCD to be 560, triangle ABD must be a multiple of a 3:4:5 triangle with sides 120, 160 and 200.
Thus:
Area of rectangle ABCD = L * W = 160 * 120 = 19200
_________________
GMAT and GRE Tutor for over 20 years
Recent success stories for my students:admissions into Booth, Kellogg, HBS, Wharton, Tuck, Fuqua, Emory and others.
Available for live sessions in NYC and remotely all over the world
For more information, please email me at GMATGuruNY at gmail