The sides of a rectangle are in the ratio 5:3 and the perimeter is 80 cm. If…
2025
The sides of a rectangle are in the ratio 5:3 and the perimeter is 80 cm. If the longer side is increased by 20% and the other side is increased by 40%, what will be the perimeter of the new rectangle?
- A.
100 cm
- B.
102 cm
- C.
106 cm
- D.
104 cm
- E.
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Correct answer: B
To find the perimeter of the new rectangle, let's break the problem down into steps.
Step-by-Step Analysis
Find the original sides:
The ratio of sides is 5:3. Let the sides be 5x and 3x.
The perimeter formula is 2 * (length + width) = 80 cm.
2 * (5x + 3x) = 80
2 * (8x) = 80
16x = 80
x = 5.
Original length = 5 * 5 = 25 cm.
Original width = 3 * 5 = 15 cm.
Calculate the new sides:
The longer side (length) is increased by 20%:
New length = 25 + (20% of 25) = 25 + 5 = 30 cm.
The other side (width) is increased by 40%:
New width = 15 + (40% of 15) = 15 + 6 = 21 cm.
Calculate the new perimeter:
New perimeter = 2 * (new length + new width)
New perimeter = 2 * (30 + 21)
New perimeter = 2 * 51 = 102 cm.