Question

The perimeter and area of a rectangular park are 50 m and 150 m² respectively. What are its dimensions?​

Answer 1

✬ Answer:

The dimensions are 15 m and 10 m

✬ Step-by-step explanation:

Given:

• Perimeter of rectangular park = 50 m
• Area of rectangular park = 150 m²

To find:

Length and breadth of park = ?

Solution:

Let:

✭ Length of rectangle be x

✭ Breadth of rectangle be y

According to the Question;

Perimeter = 50

⇒ 2(x + y) = 50

⇒ (x + y) = 50 ÷ 2

⇒ (x + y) = 25        ----- [Equation ➀]

Now, Area = 150

⇒ xy = 150

⇒ x = 150 ÷ y       ------ [Equation ➁]

Substitute the value of x from Equation ➁ in Equation ➀

$\boldsymbol{\dfrac{150}{y}+y=25}$

$\dashrightarrow \: \: \sf{\dfrac{150+y^{2}}{y}=25}$

$\dashrightarrow \: \: \sf{150 + y^2 = 25y}$

$\dashrightarrow \: \: \sf{y^2 - 25y + 150 = 0}$

$\dashrightarrow \: \: \sf{y^2 - 15y - 10y + 150 = 0}$

$\dashrightarrow \: \: \sf{(y - 15) (y-10) = 0}$

$\therefore \: \sf{y=15 \: \: or \: \: 10}$

Case 1: When y = 15,

x = 150 ÷ 15

⇒ x = 10

Case 2: When y = 10,

x = 150 ÷ 10

⇒ x = 15

Therefore, the dimensions are:

• 15 m
• 10 m

Answer 2

Step-by-step explanation:

Given:

Perimeter of rectangular park = 50 m

Area of rectangular park = 150 m²

To find:

Length and breadth of park = ?

Solution:

Let:

✭ Length of rectangle be x

Length of rectangle be x✭ Breadth of rectangle be y

According to the Question;

Perimeter = 50

⇒ 2(x + y) = 50

⇒ (x + y) = 50 ÷ 2

⇒ (x + y) = 25        ----- [Equation ➀]

Now, Area = 150

⇒ xy = 150

⇒ x = 150 ÷ y       ------ [Equation ➁]

Substitute the value of x from Equation ➁ in Equation ➀

$\boldsymbol{\dfrac{150}{y}+y=25}$

$\dashrightarrow \: \: \sf{\dfrac{150+y^{2}}{y}=25}$

$\dashrightarrow \: \: \sf{150 + y^2 = 25y}$

$\dashrightarrow \: \: \sf{y^2 - 25y + 150 = 0}$

$\dashrightarrow \: \: \sf{y^2 - 15y - 10y + 150 = 0}$

$\dashrightarrow \: \: \sf{(y - 15) (y-10) = 0}$

$\<strong>therefore</strong> \: \sf{y=15 \: \: or \: \: 10}$

Case 1: When y = 15,

x = 150 ÷ 15

⇒ x = 10

Case 2: When y = 10,

x = 150 ÷ 10

⇒ x = 15

Therefore, the dimensions are:

15 m

10 m