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

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

• L = x

Answer :

To find area first we should know value of with.

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

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

Insert Value of length and perimeter.

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

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

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

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

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

Now Let's find Area by using this formula

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

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

$: \implies \sf{} \star \underline{\underline{ Area = 15x - {x}^{2} \: cm {}^{2} }} \star$

hope it helps!