Question

A rectangle has a perimeter 64 centimeters. Its length is represented by 4x + 6 and breadth by 3x - 2 What is its length and breadth in centimeters?

• A. 20 and 12
• B. 24 and 8
• C. 19 and 13
• D. 22 and 10

Answer 1

Answer:

D. 22 and 10

Understanding Perimeter of a Rectangle

The perimeter of a rectangle is the total distance around its boundary. It is calculated using the formula:

Perimeter = 2 * (Length + Breadth)

Applying Algebraic Expressions

• The length of the rectangle is given as 4x + 6 centimeters.

• The breadth of the rectangle is given as 3x - 2 centimeters.

• The perimeter is given as 64 centimeters.

Setting up the Equation

Substitute the given values into the perimeter formula:

64 = 2 * ((4x + 6) + (3x - 2))

Solving for 'x'

1. Simplify the expression inside the parentheses:

   • (4x + 6) + (3x - 2) = 4x + 3x + 6 - 2 = 7x + 4

2. Substitute this back into the equation:

   • 64 = 2 * (7x + 4)

3. Divide both sides by 2:

   • 64 / 2 = 7x + 4

   • 32 = 7x + 4

4. Subtract 4 from both sides:

   • 32 - 4 = 7x

   • 28 = 7x

5. Divide both sides by 7 to find the value of 'x':

   • x = 28 / 7

   • x = 4

Calculating Length and Breadth

Now, substitute the value of x = 4 back into the expressions for length and breadth:

Length:

• Length = 4x + 6

• Length = 4(4) + 6

• Length = 16 + 6

• Length = 22 centimeters

Breadth:

• Breadth = 3x - 2

• Breadth = 3(4) - 2

• Breadth = 12 - 2

• Breadth = 10 centimeters