Question

find the expression for the area and perimeter of the rectangle in figure 3 ​

Answer 1

Given:-

• Length= x²+5 cm
• Breadth = x+3 cm

To Find:-

• Expression for the area and perimeter

$\large{ \sf{ \underline{Expression \: \: for \: \: perimeter}}}$

$\implies \: \: \: \: \large{ \bold{ \sf \: Perimeter \tiny({Rectangle}) = \large2(l \: + \: b) }}$

Now put the values,

$\implies \: \: \large{ \bold{ \sf Perimeter \tiny({Rectangle}) = \large2( {x}^{2} + 5 + x + 3) }}$

$\implies \: \: \: \: \large{ \bold{ \sf \: Perimeter \tiny({Rectangle}) = \large2( {x}^{2} + x + 8) }}$

$\implies \: \: \: \: \large{ \bold{ \sf \: Perimeter \tiny({Rectangle}) = \large2 {x}^{2} + 2x + 16 }}$

$\large \sf \: \underline{Expression \: \: for \: \: Area }$

$\implies \: \: \: \: \large{ \bold{ \sf \: Area \tiny({Rectangle}) = \large \: l \times b}}$

$\implies \: \: \: \: \large{ \bold{ \sf \: Area \tiny({Rectangle}) = \large \: ( {x}^{2} + 5)(x + 3) }}$

$\implies \: \: \: \: \large{ \bold{ \sf \: Area \tiny({Rectangle}) = \large \: {x}^{2}(x + 3) + 5( \times + 3) }}$

$\implies \: \: \: \: \large{ \bold{ \sf \: Area \tiny({Rectangle}) = \large \: {x}^{3} + 3 {x}^{2} + 5x + 3 }}$

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Answer 2

$\huge\red{A}\pink{N}\orange{S} \green{W}\blue{E}\gray{R} =$

Area of a rectangle is length x width (A = l x w)

Perimeter of a rectangle is P = 2l + 2w

P = 2(2x + 3) + 2w = 6x + 10

4x + 6 + 2w = 6x + 10

2w = 2x + 4

w = x + 2

∴ A = l + w = (2x + 3)(x + 2)

A = 2x^2 + 7x + 6 is the expression for the area in inches QED