Question

6. The length of a rectangle is 5 meters more than twice its width. Find the area of the rectangle, if its perimeter is 40 meters?

Answer 1

Answer:

Perimeter of rectangle =40 cm (given)

condition :- length = 2× breadth +2

⇒l=2b+2

perimeter p=2(l+b)=40

⇒2(2b+2+b)=40

⇒2(3b+2)=40

⇒6b=40−4=36

∴b=6cm

l=2×6+2=12+2=14cm

∴ length =14 cm, breadth =6 cm

Step-by-step explanation:

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Answer 2

Answer:

Area of the rectangle = 75cm²

Explanation:

Given,

Length of a rectangle is 5 more than twice its width.

$\rm \: If \: we \: assume \: the \: width \: as \: x$

$\rm \: Then, \: the \: length \: would \: be \: (2x + 5) \: cm$

We know,

Perimeter of a rectangle = 2(l + b)

Where, l denotes the length and b is the width.

So,

$\rm \: Perimeter \: of \: the \: rectangle = 2[(x) + (2x + 5)]$

But, the perimeter is 40 metres (given)

According to the question,

$\rm \implies \: 2[(x) + (2x + 5)] = 40$

$\rm \implies \: 2[x + 2x + 5] = 40$

$\rm \implies \: 2[3x + 5] = 40$

$\rm \implies \: 6x + 10 = 40$

$\rm \implies \: 6x = 40 - 10$

$\rm \implies \: 6x = 30$

$\rm \implies \: x = \dfrac{30}{6}$

$\rm \implies \: x = 5$

∴ The dimensions are :-

$\rm \bullet \: length = (2x + 5) = 2(5) + 5 = 15cm$

$\rm \bullet \: breadth = x = 5cm$

Hence, the area is :-

= l × b

Where, l is the length and b is the width

= 15 × 5

= 75cm²