The perimeter of a rectangle is 420 m. The length of the rectangle is

1.	The perimeter of a rectangle is 420 m. The length of the rectangle is 30 m more than its breadth. Find the time taken to cross it diagonally if the rate of speed is 10m/s.1. 15 seconds2. 18 seconds3. 17 seconds4. 12 seconds5. 10 seconds
Answer» Correct Answer - Option 1 : 15 seconds Given: Perimeter of rectangle = 420 m Length = Breadth + 30 m Rate of speed = 10 m/s Formula used: Perimeter of rectangle = 2 × (Length + Breadth) Length of diagonal = √(Length² + Breadth²) Time taken = Distance/Speed Calculation: Let the breadth of rectangle be x meter Then, length of rectangle = (x + 30) m Now, according to question, 2 × (x + x + 30) = 420 m ⇒ 2 × (2x + 30) = 420 m ⇒ 4x + 60 = 420 m ⇒ 4x = 360 ⇒ x = 90 Breadth = 90 m Length = (90 + 30) m ⇒ 120 m Length of diagonal = √(120² + 90²) m ⇒ √(14400 + 8100) m ⇒ √22500 m ⇒ 150 m So, Time taken = 150/10 seconds ⇒ 15 seconds ∴ The time taken to cross diagonally is 15 seconds

The perimeter of a rectangle is 420 m. The length of the rectangle is 30 m more than its breadth. Find the time taken to cross it diagonally if the rate of speed is 10m/s.1. 15 seconds2. 18 seconds3. 17 seconds4. 12 seconds5. 10 seconds

Answer» Correct Answer - Option 1 : 15 seconds

Given:

Perimeter of rectangle = 420 m

Length = Breadth + 30 m

Rate of speed = 10 m/s

Formula used:

Perimeter of rectangle = 2 × (Length + Breadth)

Length of diagonal = √(Length² + Breadth²)

Time taken = Distance/Speed

Calculation:

Let the breadth of rectangle be x meter

Then, length of rectangle = (x + 30) m

Now, according to question,

2 × (x + x + 30) = 420 m

⇒ 2 × (2x + 30) = 420 m

⇒ 4x + 60 = 420 m

⇒ 4x = 360

⇒ x = 90

Breadth = 90 m

Length = (90 + 30) m

⇒ 120 m

Length of diagonal = √(120² + 90²) m

⇒ √(14400 + 8100) m

⇒ √22500 m

⇒ 150 m

So, Time taken = 150/10 seconds

⇒ 15 seconds

∴ The time taken to cross diagonally is 15 seconds