Perimeter of a rect is 110 ft and its area is 684 sq feet. what is the length of the longer side?

Question

Perimeter of a rect is 110 ft and its area is 684 sq feet. what is the length of the longer side?

Answer 1

It's not the longer side.. it's the shorter side. Divide 684 by 110 to get the answer.

Answer 2

the sides are 19 and 36 feet long.

19x36=684

19(2)+36(2)=110

2L+2W=110 so

L=55-W

also LxW=684 thus

(55-W)x(W)=684 and

-W²+55w-684=0

plug this into the quadratic equation and you get side lengths 19 and 36

Answer 3

6.218218218218218218, etc.

take 648 and divide it by 110.

that gets you the answer.

it's the opposite of finding the area.

[multiplying 110 by the other side]

Answer 4

2x + 2y = 110, so x+y = 55, or x = 55-y

x * y = 684

or (55-y) * y = 684, or y^2-55y+684=0

using quadratic equation,

y= [-b  +/-  sqrt ( b^2 - 4*a*c) ]/ (2*a),

where a = 1, b =- 55, and c = 684 gives:

y = 36 or 19.

so x must be the other number.

Check:

36+19+36+19=110

39 * 19 = 684

Answer 5

Since P = 2L + 2W, W = 1/2(P-2L).

Given LW = 684, L(1/2((110)-2L)) = 684 should lead you to the right answer.

Taking it  a step further algebraically, L^2 -L-684=0,

so L = (1 +/- SQRT(1-4(-684)))/2.

Solving that, L = 26.66, but a quick check reveals that this is actually the shorter side since W = 1/2(P-2L) = 1/2(110-2(26.66)) = 28.34, a tad longer.