Question

The perimeter of a rectangle is 12 .
The length is 3 more than twice its
breadth. Find the length and breadth
of rectangle by substitution method.

Answer 1

Gɪᴠᴇɴ :-

The perimeter of a rectangle is 12 .

The length is 3 more than twice its

breadth.

ᴛᴏ ғɪɴᴅ :-

• Length
• Breadth

sᴏʟᴜᴛɪᴏɴ :-

Let length of Rectangle be x cm and breadth be y cm

then,

According to Question :-

• Length = 3 + 2(Breadth)

• x = 3 + 2y --(1)

• Perimeter of Rectangle = 2(l + b) = 12cm

➭ 2(l + b) = 12

➭ (l + b) = 12/2

➭ (l + b) = 6

➭ x + y = 6. --(2)

Substitute the value of x from (1) in (2) , we get,

➭ x + y = 6

➭ (3 + 2y) + y = 6

➭ 3 + 3y = 6

➭ 3(1 + y) = 6

➭ y + 1 = 6/3

➭ y + 1 = 2

➭ y = 2 - 1

y = 1cm

Put y = 1 in (1) , we get,

➭ x = 3 + 2y

➭ x = 3 + 2×1

➭ x = 3 + 2

➭ x = 5cm

Hence,

• Length = x = 5cm
• Breadth = y = 1 cm

Answer 2

Given:

The perimeter of a rectangle is 12 .

The length is 3 more than twice its

breadth.

to find:

Find the length and breadth

of rectangle by substitution method.

STEP BY STEP EXPLANATION:

Length of the rectangle = l

breath of the rectangle = b

l = 2 + 2b

perimeter of rectangle = 12 m

2(l+b) = 12

2(3+2b+b) = 12

2(3+3b) = 12

3 + 3b = 6

3b = 3

$\boxed{\text{b = 1}}$

Now,

L = 3 + 2

$\boxed{\text{l = 5}}$

∴ thus length = 5m bredth = 1 m

Hence verified !