aljatar
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 23861 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 23849 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