Question

The perimeter of a rectangle is 30 cm and its length is x cm. Find its area in terms of x. step by step explanation.​

Answer 1

Step-by-step explanation:

p =30cm. l= x cm

we know tha p of a rectangle = 2(l+b)

p. = 2 ( x + b)

30. = 2 ( x + b) ( given p =30cm)

2 ( x + b) = 30

x+b. = 30/2

x+b = 15

b= 15-x

therefore breadth of the rectangle is 15-x cm

area of rectangle = length x breadth

a. = x *(15-x)

= x*15 - x*x

= 15x - x²

therefore area of rectangle in terms of x = -x²+15x

Answer 2

Question:

The perimeter of a rectangle is 30 cm and its length is x cm. Find its area in terms of x.

To find:

Area in terms of x

Given:

Perimeter = 30 cm

Length = x

Answer :

To find area first we should know value of with.

So first Let's find width by using this formula:

$\red{\boxed { \sf \underline {Perimeter=2(Length+Width)}}}$

Insert Value of length and perimeter.

$:\implies \sf 30 = 2(x + width)$

$:\implies \sf \dfrac{30}{2} = (x + width)$

$:\implies \sf{}x + width = \dfrac{ { \cancel{30}}^{ \: 15} }{ { \cancel{2}}^{ \: 1} }$

$:\implies \sf{}x + width = 15$

$:\implies \sf{} \underline{\underline{ width = 15 - x}}$

Now Let's find Area by using this formula...

$\pink{\boxed { \sf \underline {Area=Length \times Width }}}$

$: \implies \sf{}Area = x \times (15 - x)$

$: \hookrightarrow\sf{} \underline{\underline{ Area = 15x - {x}^{2} \: ~~cm {}^{2} }}$