PDF800 SET3 Question 31

[zozo123]

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

[UmanG]

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)

[zozo123]

Great !!!

Thanks UmanG

[lalitgmat]

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.

[gabriel]

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 ..

[beny]

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+

[lalitgmat]

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

Find Area of Rectangular field.

[UmanG]

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-