Question

$the \: breadth \: of \: the \: rectangle \: is \: 15 m \: less \: than \: its \: length \: the \: perimeter \: of \: the \: rectangle \: is \: 430m \: find \: the \: area \: of \: the \: rectangle$
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Answer 1

Question:-

The breadth of the rectangle is 15 m less than its length. The perimeter of the rectangle is 430 m. Find the area of the rectangle.

Given:-

• Breadth of the rectangle is 15 m less than its length
• Perimeter of rectangle = 430 m

To find:-

• Area of the rectangle.

Assumption:-

• Let the length of the rectangle be x
• Breadth = x - 15

Solution:-

It is given that the perimeter of the rectangle is 430 m

We know,

✭ Perimeter of the rectangle = 2(Length + Breadth)

Hence,

430 = 2[(x) + (x - 15)]

=> 430/2 = x + x - 15

=> 215 = 2x - 15

=> 2x = 215 + 15

=> 2x = 230

=> x = 230/2

=> x = 115

Now,

Putting respective values:-

Length = x = 115 m

Breadth = x - 15 = 115 - 15 = 100 m

Now,

We know,

✭ Area of rectangle = (Length × Breadth) sq.units

Hence,

Area = (115 × 100) m²

=> Area = 11500 m²

Therefore the Area of the rectangle is 11500 m².

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Formulas Used:-

• Area of rectangle = (Length × Breadth) sq.units

• Perimeter of rectangle = 2(Length + Breadth) units.

________________________________

Answer 2

Given:–

• Breadth of the rectangle is 15m less than its length
• Perimeter of rectangle = 430m

To Find:–

• Area of the rectangle.

Formulas Used:–

• (i) Area of rectangle = Length × Breadth.
• (ii) Perimeter of rectangle = 2 (l + b) units.

Required Solution:–

• Let's assume the length of the rectangle as x
• Then Breadth = x – 15

Here formula (i) is used :

• Perimeter of the rectangle = 2(l + b)

According to the Question,

$\\ \sf 430 = 2[(x) + (x - 15)] \\ \\ \sf ➟ \: \frac{430}{2} = (x + x) - 15 \: \\ \\ \sf ➟ \: 215 = 2x - 15 \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf➟ \: 2x = 215 + 15 \: \: \: \: \: \: \: \: \: \: \\ \\ \sf➟ \: 2x = 230 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: ➟ \: x = \frac{230}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \\ \\ \sf➟ \: x = { \underline {\boxed{ \bf{ \pink {115}}}} }\bigstar \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

So,

• Length of the rectangle ➟ x = 115 m
• Breadth ➟ x - 15 = 115 - 15 = 100 m

Here formula (ii) is used

• Area of rectangle = (l × b) sq.units

$\\ \sf \: Area = (115 × 100) m² \\ \\ \sf ➟Area = 11500 m² \: \: \:$

${ \boxed{ \therefore{ \underline{ \bf{ \purple{The \: Area \: of \: the \: rectangle \: is \: 11500 m².}}}}}}$