Problem Solving

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

Let's assume length of one side is X, thus ractanguler has 2 sides of length X and another 2 sides of length 280-X...

Now Area of ract. = X(280-X) = 280X - X^2.....(1)

Diagonal will create 2 trinagle with hyotenuse of length 200...
Using pythagora will get following equation,
X^2 + (280-X)^2 = 200^2
--> 2X^2 + 280^2 - 560X = 200^2
--> X^2 + 280*140 - 280X = 20000
-->19200 = 280X - X^2
-->19200 = Area of ract. from (1)

Great !!!

Thanks UmanG

If I twist the question for a 700+;
A small, rectangular park has a perimeter of 560 feet and One side of park is lesser than adjacent side by X feet. What's the Area of Park.

lalitgmat wrote:If I twist the question for a 700+;
A small, rectangular park has a perimeter of 560 feet and One side of park is lesser than adjacent side by X feet. What's the Area of Park.

cant answer ..

.. the eqn is 2( a + (a+x)) = 560 .. so two variables and one eqn ..

lalitgmat wrote:If I twist the question for a 700+;
A small, rectangular park has a perimeter of 560 feet and One side of park is lesser than adjacent side by X feet. What's the Area of Park.

Plus... you already assume that one side is less than the other side by X feet... why would you ever need to state that in the question? This is like twisting it to 200-, not 700+

My Mistake. Question I meant is.
Rectangular perimeter = 560feet
Differnce between sides is 200feet.

Find Area of Rectangular field.

Let's assume a side has length X. And difference in length between 2 side is 200 means another side will be X+200.

simply X+X+200 = 280 which leads to X = 40.
Area = 40 * (40+200)

Don't you think this is more easier one....
May be as beny told 200-