Find the dimensions of a rectangle?

Question

Find the dimensions of a rectangle whose perimeter is 46 cm and whose area is 120 cm square.

Answer 1

Let L be the length.
Let W be the width

The perimeter is given by:
2L + 2W = 46
L + W = 23
W = 23 - L

The area is given by the formula:
A = LW

Substitute in A = 120, W = 23 - L
120 = L(23 - L)

Expand:
120 = -L² + 23L

Move to the other side:
L² - 23L + 120 = 0

Factor:
(L - 8)(L - 15) = 0

So length = 8 or 15
and width = 15 or 8

The dimensions are 8 cm x 15 cm

(Double-check, perimeter = 2(8) + 2(15) = 46 cm, area = 8 x 15 = 120 cm²)

Answer 2

L x W = AREA
L + L + W + W = PERIMETER

2L+ 2W = PERIMETER
2L+ 2W = 46
2 (L + W) = 46
L + W = 23

L x W = 120

What two numbers multiply to give you 120, but add up to be 23? So you find the factors of 120:

1, 120
2, 60
3, 40
4, 30
5, 24
6, 20
8, 15
10,12

Those are the factors, so you can start adding up the factors:

1 + 120 = 121 NO
2 + 60 = 62 NO

The only one that equals 23 when added is 8 and 15.

8 + 15 = 23

The dimensions of the rectangle are 8 cm by 15 cm.

Answer 3

The dimensions on the rectangle are 15 X 8 =120. If you add 15+8 +8 +15, you get 46 which is your perimeter. Length x width = area. Just plug in numbers and see what ones work. There may be a simpler way but this is how I would do it.

Answer 4

Given: P=46 cm A=120 cm square
Solution:
P=2L + 2W (equation 1)
A= LW (equation 2)
from equation 1:
46= 2L+2W therefore, L=23-W(equation 3)
substituting equation 3 in equation 2:
120= (23-W)W
using quadratic equation:
W=8 cm and L= 15 cm

Answer 5

46 cm = 2L + 2W and
Solving for L
L = 23 - W

also,
120 = L * W

substitute the first value of L into the above equation, and

120 = (23 - W) * W
120 = 23W - W^2

Solve the polynomial for W,

W = 15 and L = 8
or the other way around if you prefer.

Answer 6

x = length of 1 side, y = length of another side

Values of another side (y):
2(x + y) = 46
x + y = 23
y = 23 - x

xy = 120
y = 120/x

Value of one side (x):
23 - x = 120/x
23x - x^2 = 120
x^2 = 23x - 120
x^2 - 23x + 120 = 0
(x - 8)(x - 15) = 0

x = 8, 15

Answer: The sides are 8 and 15 cm.

Proof (perimeter is 46 cm):
= 2(8 cm + 15 cm)
= 2 * 23 cm
= 46 cm

Proof (area is 120 square cm):
= 8 cm * 15 cm
= 120 square cm

Answer 7

2w + 2l = 46 [1]
wl = 120 [2]

w = 120/l
substitute to [1]
2(120/l) + 2l = 46
240/l + 2l = 46
Multiply by l
240 + 2l^2 = 46l
l^2 - 23l + 120= 0
l = (23 +- sqrt(529 -480))/2 = (23+- 7)/2 = 15 , 8
w = 8, 15
therefore 15 x 8 cm

Answer 8

area = width * length
120 = w * l ..(1)

perimeter = (width + length) 2
46 = (w + l)2
23 = w + l
w = 23 - l ...(2)

sub (2) into (1)
120 = (23 - l) l
120 = 23l - l^2
l^2 - 23l +120 = 0
(l - 8) (l - 15) = 0
l = 8 or 15

Sub l = 8 or 15 into (2)
w = 15 or 8

That mean when length is 8cm, width is 15cm.
And length is 15cm, width is 8cm.

Answer 9

1)2x+2y=46

x+y=23

2)xy=120
x=120/y

substitute120/y +y=23
multiply both sides by y
120+y^2=23y
y^2-23y+120=0
use quadratic equ to solve for y
y=23+-sqrt(23^2-480)/2=23+-sqrt49/2=15,8
the dimension is 15 cmx8cm

Answer 10

using the factors of 120... 1,120 2,60... 3,40... 4,30... 5,24.. 6,20... 8,15... and 10,12 you can plug them into the formula 2w+2L=120.. the answer that way would be 8 and 15

8X15 rectangle