Question 15 of 49intermediate🔧 ApplyNumerical3 marks

If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?

Correct Answer

Length = 9 cm, Width = 3 cm

Exercise: Exercise Set 2.2 | Q: 7 | (Page 6)
For More Understanding

Explanation

The problem requires setting up a linear equation based on the given word problem. By defining the width as a variable 'w', the length can be expressed as '2w + 3'. Using the standard perimeter formula for a rectangle, we substitute the expressions and the given perimeter value to solve for the variable, and subsequently find the length.

Solution Steps

  1. Step 1: Let the width of the rectangle be ww cm. Then, the length is (2w+3)(2w + 3) cm.

  2. Step 2: The perimeter of a rectangle is 2(length+width)2(\text{length} + \text{width}). Given perimeter is 24 cm, so 2(w+2w+3)=242(w + 2w + 3) = 24.

  3. Step 3: Simplify the equation: 2(3w+3)=242(3w + 3) = 24, which gives 3w+3=123w + 3 = 12.

  4. Step 4: Solve for ww: 3w=93w = 9, so w=3w = 3 cm.

  5. Step 5: Calculate the length: 2w+3=2(3)+3=92w + 3 = 2(3) + 3 = 9 cm.

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