A rectangular ink pad has a perimeter of 20 centimeters. Its area is 24 square centimeters. What are the dimensions of the ink pad?

Method 1:
Let x centimeters by (24/x) centimeters be the dimensions of the ink pad.

2 [x + (24/x)] = 20
x + (24/x) = 10
For x ≠ 0:  [x + (24/x)] x = 10x
x² - 10x + 24 = 0
(x - 4)(x- 6) = 0
x = 4 or x = 6

The answer: 4 centimeters by 6 centimeters

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Method 2:
Let x centimeters by y centimeters be the dimensions of the ink pad.

2(x + y) = 20 …… [1]
xy = 24 …… [2]

From [1]:
x + y = 10
x = 10 - y …… [3]

Substitute [3] into [2]:
(10 - y)y = 24
y² - 10y + 24 = 0
(x - 4)(x - 6) = 0
x = 4 or x = 6

Substitute the value of x into [3]:
When x = 4: y = 6
When x = 6: y = 4

The answer: 4 centimeters by 6 centimeters

PERIMETER = 2 ( LENGTH + BREADTH ) = 20 CM

LENGTH + BREADTH = 10 CM

LET THE BREADTH BE  X  CM

LENGTH = 10- X   CM

( 10 - X ) * X =  24 SQ CM

10X - X^2 = 24

X^2 -10X + 24=0

( X-6) ( X-4) = 0

X = 4

BREADTH = 4 CM  LENGTH = 6 CM ANSWER

Let L be length and W be width. 
 2L + 2W = 20, and LW = 24. L = 24/W.  
2(24/W) + 2W = 20
48/W + 2W = 20
48 + 2W^2 = 20W.
2W^2 - 20W + 48 = 0
W^2 -10W + 24 = 0
(W - 6)(W - 4) = 0
W = 6; L =24/W = 24/6 = 4.
Dimensions are 4 and 6.

Given 
A = 24 cm^2
P = 20 cm

P = 2l + 2w
20 = 2l + 2w eq1

A = lw
24 = lw eq2

at eq2 make l as the subject.

l = 24/w

substitute l l = 24/w to eq1

[20 = 2(24/w) + 2w]w
20w = 48 + 2w^2
2w^2 - 20w + 48 = 0
 w^2 - 10w + 24 = 0
(w - 4)(w - 6) = 0
w = 4, w = 6

solving its length from eq2.

when w = 4

l = 24/4 = 6 cm

when w = 6

l = 24/6 = 4 cm

4 centimeters by 6 centimeters ....//

AnswerSave

2l + 2w = 20
==> l+w = 10
==> l = 10-w
...l*w = 24==> w(10-w) = 24==> 10w - w^2 = 24==> w^2 -10w + 24 = 0==> (w-4)(w-6) = 0==> w = 4 or 6 cmand l = 6 or 4 cmSo, 6 by 4 cm

Area = Length x Width
A = L X W
If the area is 24, you have to figure out what 2 numbers multiplied = 24
1 x 24
2 x 12
3 x 8
4 x 6
Perimeter = lenght + width + length + width
Perimeter = 2 length + 2 width
P = 2L + 2W
now draw a rectangle and plug these numbers in to find the perimeter 24
the first option is wrong because you already see 24 and if you add them up it will go higher than 20
2 + 2 + 12 + 12 = 28
3+3+8+8 =22
4+4+6+6 = 20 bingo, so your length and your width are 4 and 6!
the rule of perimeter that i gave is only valid for a rectangle or square
do not use this rule for other shapes 
The answer is 4x6

4 centimeters by 6 centimeters.

6 centimeters by 4 centimeters

Nearly equal factors of area 24 are 4*6
That works with 2(4 + 6) so answers were by inspection

4cm by 6cm=
P=4+4+6+6=20
A=4 * 6 = 24

A rectangular ink pad has a perimeter of 20 centimeters. 
Its area is 24 square centimeters. 
What are the dimensions of the ink pad?
The length is 6 cm and the width is 4 cm.