Question

1. ara.
Length of rectangle is 10 cm more than twice of breadth. Perimeter is 560 cm. Find Length and breadth and also find area.​

Answer 1

Answer:

• Length of rectangle is 190 cm.
• Breadth of rectangle is 90 cm.
• Area of rectangle is 17100 cm².

Step-by-step explanation:

Given :-

• Perimeter of rectangle is 560 cm.

To find :-

• Length and breadth of rectangle.
• Area of rectangle.

Solution :-

Let, Breadth of rectangle be x cm.

And, Length of rectangle be 2x + 10 cm. [We take length be 2x + 10 cm because it is given that length is ten cm more than twice the breadth]

Now,

Perimeter of rectangle = 2(Length + Breadth)

Put the values :

$\longrightarrow$ 560 = 2 × (2x + 10 + x)

$\longrightarrow$ 560 = 4x + 20 + 2x

$\longrightarrow$ 560 = 6x + 20

$\longrightarrow$ 560 - 20 = 6x

$\longrightarrow$ 540 = 6x

$\longrightarrow$ 540/6 = x

$\longrightarrow$ x = 90

Verification :-

$\longrightarrow$ 560 = 2(2x + 10 + x)

• Put x = 90.

$\longrightarrow$ 560 = 2(2 × 90 + 10 + 90)

$\longrightarrow$ 560 = 2(180 + 10 + 90)

$\longrightarrow$ 560 = 2(190 + 90)

$\longrightarrow$ 560 = 380 + 180

$\longrightarrow$ 560 = 560

$\boxed{\sf Hence \: Verified.}$

We take :

Breadth be x. So, Breadth of rectangle is 90 cm.

Length be 2x + 10 = 2 × 90 + 10 = 190. Thus, Length of rectangle is 190 cm.

We know,

Area of rectangle = Length × Breadth

So,

$\longrightarrow$ Area = 190 × 90

$\longrightarrow$ Area = 17100

Therefore,

Area of rectangle is 17100 cm².

Answer 2

Given :

⬤ Length of Rectangle is 10 cm more than twice of Breadth .

⬤ Perimeter of Rectangle is 560 cm.

To Find :

⬤ Length and Breadth of Rectangle .

⬤ Area of Rectangle.

Formula Used :

$\bf[\:{Perimeter \: of \: Rectangle = 2(l+b)}\:]$

Solution :

Let :

• Breadth of Rectangle be x.
• Length of Rectangle be 2x + 10.

According to the Formula :-

560 = 2(l + b)

560 = 2(2x + 10 + x)

560/2 = 3x + 10

280 = 3x + 10

280 - 20 = 3x

270 = 3x

270/3 = x

90 = x

Therefore , Value of x is 90 .

Hence ,

Length of Rectangle = 2x + 10

= 2(90) + 10

= 180 + 10

= 190

Breadth of Rectangle = x

= 90

Therefore , Length and Breadth of Rectangle are 190 cm and 90 cm.

Formula Used :

$\bf[\:{Area \: of \: Rectangle = L \times{b}}\:]$

Now :

• Length = 190 cm
• Breadth = 90 cm

According to the Formula :-

L × b

190 × 90

17100

Therefore , Area of Rectangle is 17100 cm².