Question

Q4. The length of a rectangle is 5 cm. less than twice its breadth. If the length is
decreased by 3cm and breadth is increased by 2 cm, the perimeter of the resulting
rectangle is 72cm. Find the dimensions of the rectangle.​

Answer 1

✬ Length = 23 Cm ✬

✬ Breadth = 14 Cm ✬

Step-by-step explanation:

Given:

• Length of rectangle is 5 cm less than twice it's breadth.
• Length is decreased by 3 cm and Breadth is increased by 2 cm then perimeter is 72 cm.

To Find:

• What is the length and breadth of rectangle?

Solution: Let length of rectangle be x cm and breadth be y cm.

A/q

• Length = x = 2y – 5

• Length is decreased by 3 cm •

$\small\implies{\sf }$ New Length = (x – 3)

• Breadth is increased by 2 cm •

$\small\implies{\sf }$ New Breadth = (y – 2)

★Perimeter of Rectangle =2(Length + Breadth)★

$\small\implies{\sf }$ Perimeter = 2 ( x – 3 + y – 2)

$\small\implies{\sf }$ 2x – 6 + 2y – 2 = 72 [ Divide all terms by 2 ]

$\small\implies{\sf }$ x – 3 + y – 1 = 36

$\small\implies{\sf }$ 2y – 5 + y = 36 + 1 [ Since, x = 2y – 5 ]

$\small\implies{\sf }$ 3y – 5 = 37

$\small\implies{\sf }$ 3y = 37 + 5

$\small\implies{\sf }$ y = 42/3

$\small\implies{\sf }$ y = 14 cm

Hence, The breadth of rectangle is y = 14 cm and Length of rectangle is x = 2y – 5

→ x = 2 x 14 – 5

→ x = 28 – 5

→ x = 23 cm

Answer 2

$\huge\underline\mathfrak\orange{Answer:-}$

⚫ Length $\implies$ 23 cm

⚫ Breadth $\implies$ 14 cm

$\huge\underline\mathrm{ GivEn:-}$

⭐ length of a rectangle is 5 cm less than twice its breadth

⭐ length is decreased by 3cm and breadth is increased by 2 cm

$\huge\underline\mathrm{ Need \:to\: find:-}$

➡ Length And Breadth of the rectangle = ?

$\huge\underline\mathrm{SoLution:-}$

➡ Let the length and breadth of the rectangle be 'l' and 'b' cm respectively.

⚫According to question :-

$\implies$ l = 2b - 5 ___1)

⭐ If the length is reduced by 3 cm

↪ New Length $\longrightarrow$ (l-3) cm

⭐ If the breadth is increased by 2 cm

↪ New Breadth $\longrightarrow$ (b+2) cm

⚫If the length is decreased by 3cm and breadth is increased by 2 cm, the perimeter of the resulting rectangle is 72cm

⭐ Perimeter of rectangle$\implies$ 2[l+b]

⚫According to question :-

$\implies$ 2[(l-3)+(b+2)]=72

$\implies$ 2[(2b-5-3)+(b+2)]=72(__ from equation 1)

$\implies$ 2[(2b-8)+(b+2)]=72

$\implies$ 2[2b-8+b+2]=72

$\implies$ 2[3b -6]=72

$\implies$ 3b -6=36

➡ Divide the equation by '3'

$\implies$ b-2=12

$\implies$ b=14 cm

⭐ On putting the value of 'b' in eq. 1, we get,

$\implies$ l = 2(14)-5

$\implies$ l = 28-5

$\implies$ l = 23 cm

⭐ Hence, the length and breadth of the rectangle are 23 and 14 cm respectively.

$\huge\underline\mathfrak\orange{Thanks..}$