Rectangle, The long sides are 2 in longer than the short sides the area of the board is 288in, find the sides.

Question

Please explain your work. . .

Answer 1

ok. let the short sides have length x and the long sides have lengths x + 2 (since they are 2 in longer)

area = length * width

thus (x) * (x + 2) = 288 in

so x^2 + 2x = 288

solve for x

x=16

so now, you know the short side is 16, since we've defined it as x, and the long side is 18, since it is x + 2.

to double check, 16 * 18 = 288. sweeeetness.

Answer 2

Area = L x W

L = W+2

A = 288 = (W+2)W
288 = W^2 + 2W

Completing the square,

W^2+2W - 288 = 0

or W^2 + 2W - (-1 + 289) = 0

W^2 + 2W + 1 - 289 = 0
(W+1)^2 = 289

Taking the square root on both sides

(W+1) = 17 (using the positive solution only)

W = 16
L=W+2 = 18

A = 16*18 = 288

Good luck!

Answer 3

let x be the shorter side
x+2 would equal the longer side

since area is the longer side multiplied by the shorter side, the formula is

x(x+2)=288
x^2+2x=288
x^2+2x+1=289
(x+1)^2=289
(x+1)=17
x=16

In order to solve this equation, i had to find a x^2+2xy+y^2 in order to square root it into (x+y)^2, and square root the other side.

Now that you have found x, which is the shorter side, simply add 1 to x to find the longer side

Answer 4

x(x+2) = 288

x^2 + 2x = 288

x^2 + 2x - 288 = 0

quadratic formula time

-2 +/- sqrt(4-4(1)(288))
----------
2


-2 +/- 34
------
2

answers: x = 16 or -18

sicne there is no negative length, throw the negative answer out

so x (the short sides) is 16in and since the long sides are 2 inches longer that would make them 18in.

now lets check our work

16*18 = 288

yayness

Answer 5

One side is x the other x+2 and
x*(x+2) = 288
x² + 2x = 288
x² + 2x -288 = 0
(x-16)*(x+18) = 0
so
x = 16 and the sides are 16 and 18 inches.
(the other answer, x = -18 is called an 'extraneous' root)

Hope that helps.


Doug

Answer 6

w: x
L: x+2


a=wL
288 = x(x+2)
288 = x^2 + 2x
x^2 + 2x - 288 = 0
(x-16)(x+18)
x= 16

W=16in
L= 18in

Answer 7

the ans is 18in n 16in.

Answer 8

_____________
|_____________|
|_____________| L = x
|_____________|
w = x+2

area = W * L

288 =(x)(x+2)
288=x^2 +2x