Question

Express the perimeter P of a square with side x as a function of its area

Answer 1

Answer:

a. s²

b. p²÷16

Step-by-step explanation:

a. let s be the side of the square.

let A be the area of the square.

let P be the perimeter of the square.

A= s×s= s²

b. p= 4s

A= s²

A = (4s×4s) ÷ 16

A= p²÷ 16

Answer 2

SOLUTION

TO DETERMINE

Express the perimeter P of a square with side x as a function of its area

EVALUATION

Here it is given that the side of the square = x

Let Perimeter = P and area = A

Then

Perimeter = 4 × Side

⇒ P = 4x - - - - - - (1)

Area = (Side)²

⇒ A = x² - - - - - - (2)

Squaring both sides of Equation 1 we get

P² = 16x²

⇒ P² = 16A [ Using Equation 2 ]

$\displaystyle \sf{ \implies A = \frac{ {P}^{2} }{16} }$

FINAL ANSWER

Hence the required function is

$\displaystyle \sf{ A = \frac{ {P}^{2} }{16} }$

Where Perimeter = P and area = A

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