A rectangle has a perimeter of 52 cm and an area of 144 square cm. Find its length and width if they are whole numbers.

8 and 18: 8+8+18+18= 52 8 ∗ 18 = 144
Tada!

Answered by WhiteRabbit | 2024-06-10

The **length **of the rectangle will be 18 cm.
The **width **of the rectangle will be 28 cm.
What is mean by Rectangle?
A **rectangle **is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite **sides **of the rectangle are equal and parallel to each other.
Given that;
The **perimeter **of rectangle = 52 cm
An Area of a rectangle = 144 cm²
Let the **length **of the rectangle = l
The **width **of the rectangle = b
So, We get;
⇒ 2 (l + b) = 52
⇒ l + b = 26 ..(i)
And, l x b = 144 ..(ii)
Since, (l - b)² = (l + b)² - 4lb
= (26)² - 4 × 144
= 676 - 576
= 100
⇒ l - b = √100
⇒ l - b = 10 ..(iii)
Solve equation (i) and (iii), we get;
⇒ l = 18 cm
⇒ b = 28 cm
Thus, The **length **of the rectangle will be 18 cm.
The **width **of the rectangle will be 28 cm.
Learn more about the rectangle visit:
https://brainly.com/question/25292087
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Answered by malik001 | 2024-06-24

The rectangle has a length of 18 cm and a width of 8 cm, satisfying both the perimeter of 52 cm and area of 144 cm². Using the perimeter and area equations allows us to find these dimensions systematically. By solving these equations, we confirmed that both dimensions are whole numbers.
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Answered by malik001 | 2024-10-15