Math question help!?

Question

The area of the floor is 880 sqm. and its perimeter is 124m. Find its length and width!..
help me!

Answer 1

I assume the floor is a rectangle. We have two unknowns, L and W. The area is LW and the perimeter is 2L + 2W. Both are given, so we have two equations in two unknowns.

LW = 880
2L + 2W = 124

Rewrite the first equation as W = 880/L. Now use this expression to rewrite the second equation as

2L + 2(880/L) = 124
L + 880/L = 62
L^2 + 880 = 62L
L^2 - 62L + 880 = 0
(L - 22)(L - 40) = 0
L = 22 or L = 40

We already know that W = 880/L, so W = 880/22 or 880/40 = 40 or 22. That is to say, either L = 22 and W = 40 or L = 40 and W = 22. That is to say, the dimensions of the room are 40 m by 22 m. The two solutions are interchangeable, although we normally call the larger dimension length, so L = 40 and W = 22 is probably the more correct response.

Answer 2

GIVEN:
2( Length + width) = 124
Lw = 880

L + w = 62
L + 880/L = 62
L^2 - 62L + 880 = 0
(L - 40)(L -22) = 0
Length = 40 width = 22

Answer 3

Let L = length, W = width

LW = 880
L = 880/W

2(L + W) = 124
L + W = 124/2
L + W = 62
L = 62 - W

880/W = 62 - W
880/W - 62 = - W
W = 62 -880/W
W = 22

L = 62 - 22
L = 40

Answer: length = 40 m, width = 22 m.

Proof:
Area:
40 * 22 = 880
Perimeter:
2(40 + 22) = 124
2(62) = 124
124 = 124

Answer 4

length = L
width = w
2( L + w) = 124
Lw = 880

L + w = 62
L + 880/L = 62
L^2 - 62L + 880 = 0
(L - 40)(L -22) = 0

L = 40 width = 22

Answer 5

LW = 880
2L + 2W = 124
multiply the second by L to get

2LL + 2LW = 124L

Now, multiply the first by 2 and subtract it from above to get

2LL = 124L - 1760
rearrange to the form of a quadratic equation:

2LL - 124L + 1760 = 0 and find the roots from the quadratic formula.