The area of a rectangle is 192 cm(square) and its perimeter is 56 cm .find the dimensions of the rectangle.?

Answer 1

56/4 =14 average length of a side
(14+X) *(14-X) =192
-X^2 + 196 = 192
X^2 = 4
X= + or - 2
Dimentions are 16cm by 12cm

Answer 2

The area of a rectangle = l x b = 192 cm(sq)
= l = 192/b
The perimeter = 2l + 2b = 56
= 2*(192/b) + 2b = 56
= (384/b) +2(b^2) =384
rearranging&dividing by 2 = b^2 - 28b + 192 =0
= b^2 - 16b - 12b + 192 = 0
= b(b - 16) - 12(b - 16) = 0
= (b - 16) (b -12) =0
so b-16=0 i.e b= 16
or
b-12 = 0 i.e b = 12
if l = 12 then b = 16 or vice versa

area = l * b = 12 * 16 = 192
peri = (2 *12)+(2 * 16) = 24 +52 = 56

Answer 3

Let
l = length of the rectangle
w = width of the rectangle
A = 192 cm² = lw
P = 56 cm = 2l + 2w

2l + 2w = 56 cm
l + w = 28 cm
l = 28 cm - w

substitute this to the first equation (the area equation)
(28 cm - w)(w) = 192 cm²
28 cm w - w² - 192 cm² = 0
w² - 28 cm w + 192 cm² = 0
(w - 16 cm)(w - 12 cm) = 0
w = 16 cm, w = 12 cm
solving for the other,
l = 12 cm, l = 16 cm

Obviously the only pair that makes sense is when l = 16 cm and w = 12 cm, because the tradition is that the length is greater than the width.

Therefore, the dimensions of the rectangle is 16 cm and 12 cm.

^_^

Answer 4

Area = 192 cm^2 = l*b
ie, l = 192/b (1)
Perimeter = 56 cm = 2(l + b)
ie. , 2l + 2b = 56
l + b = 28
l = 28 - b (2)
equation (1) is equal to equation (2)
Therefore, 192/b = 28 - b
192 = b(28 - b)
b^2 - 28b + 192 = 0
(b - 12)(b - 16) = 0
b = 12 or b = 16
Since breadth is shorter than length,
b = 12
Then, l = 28 - b = 16
Therefore the dimensions are
12 cm x 16 cm

Answer 5

let x & y be the lengths of the sides of the rectangle

xy = 192 or y = 192/x
2x + 2y = 56

2x + 2(192/x) = 56
x + 192/x = 28
x^2 + 192 = 28x
x^2 - 28x + 192 = 0
(x-16)(x-12) = 0
x = 16 or x = 12

therefore, the dimension of the rectangle is 16 cm X 12 cm

Answer 6

let x = length; y = width

xy = 192
2x + 2y = 56
x + y = 28
x = 28 - y

(28 - y)y = 192
28y - y^2 = 192
0 = y^2 - 28y + 192
0 = (y - 16)(y - 12)
y = 12 or 16 (must be 12 since x > y)

x + 12 = 28
x = 16

The rectangle is 16 cm long and 12 cm wide.

Answer 7

Area= l * b l=length b=breadth

l*b=192----eq-1

2(l+b)=56 ..........eq-2

from 1 b=192/l

substituting in eq 2
2(l+192/l)=56
2((l(sqr)+192)/l)=56
2l(sqr)+384=56l
l(sqr)-28l+192=0
l=12 l=16

Answer 8

lw = 192
2(l + w) = 56

lw = 192
l + w = 28

l + w = 28
w = -l + 28

(-l + 28)l = 192
-l^2 + 28l = 192
-l^2 + 28l - 192 = 0
-(l^2 - 28l + 192) = 0
l^2 - 28l + 192 = 0
(l - 12)(l - 16)

l = 16

w = -16 + 28
w = 12

Length = 16cm
Width = 12cm

Answer 9

width x length = 192
2 ( width + length ) = 56
width + length = 28
width = 28 - length
then :
(28 - length) x length = 192
28 length - length^2 =192
Length^2 - 28 length +192 = 0
(Length - 16) (Length - 12 ) = 0
So..
Length = 16 cm
and width = 28 - 16 = 12 cm

Answer 10

2X + 2Y = 56

X * Y = 192 ...........> X = 192/y

COMBINING EQUATIONS

2(192/Y) + 2Y = 56..........> 192 + Y^2 = 28Y

Y^2 - 28Y +192 = 0

(Y-16)*(Y-12) = 0..........> Y = 16 OR 12

DIMENSIONS OF RECTANGLE ARE 12 AND 16