QUESTION 7
Easy
If the length of a rectangle is three more than twice its width and its perimeter is 24cm, what are the dimensions of the rectangle?
SOLUTION
1
Assume the width and length of the rectangle
Let the width of the rectangle be \(w\) cm. Then its length will be \(2w + 3\) cm (three more than twice the width).
2
Form the equation by substituting the assumed width and length into the formula of perimeter of a rectangle and solve for w
Perimeter \( = 2 × (length + width) = 24 \)cm
⇒ \(2 × ((2w + 3) + w) = 24\)
⇒ \(2 × (3w + 3) = 24 \)
⇒ \( 3w + 3 = 12\)
⇒ \(3w = 9\)
⇒ \(w = 3\)
⇒ \(2 × ((2w + 3) + w) = 24\)
⇒ \(2 × (3w + 3) = 24 \)
⇒ \( 3w + 3 = 12\)
⇒ \(3w = 9\)
⇒ \(w = 3\)
3
Write the dimensions of the rectangle
width \( = w = 3\) cm
length \( = 2w + 3 = 6 + 3 = 9\) cm
length \( = 2w + 3 = 6 + 3 = 9\) cm
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Final Answer : The width of the rectangle is 3cm and its length is 9cm.
Concept Note
Let the width be \(w\) and express length as \(2w + 3\). Substitute these into perimeter formula (2(l + w))= given value, solve for \(w\) and then find length.