The diagram shows triangle \(ABC\) with \(AB = 10\) cm, \(BC = 8\) cm and \(AC = 12\) cm. Triangle \(ABC\) is enlarged with scale factor \(1.75\). Calculate...
Question 1 Report
The diagram shows triangle \(ABC\) with \(AB = 10\) cm, \(BC = 8\) cm and \(AC = 12\) cm.
Triangle \(ABC\) is enlarged with scale factor \(1.75\).
Calculate the perimeter of the enlarged triangle.
Answer Details
Perimeter is a total of lengths, so it scales in exactly the same way as any single length: multiply by the scale factor once, not by its square. That makes a shortcut available, since you can enlarge the whole perimeter in one step instead of enlarging each side separately.
- Find the perimeter of the original triangle: \[ 10 + 8 + 12 = 30 \text{ cm} \] [M1]
- Multiply by the scale factor: \[ 30 \times 1.75 \] [M1]
- \( = 52.5 \)
The perimeter of the enlarged triangle is \( 52.5 \) cm. [A1]
The longer route confirms it: the enlarged sides are \( 10 \times 1.75 = 17.5 \) cm, \( 8 \times 1.75 = 14 \) cm and \( 12 \times 1.75 = 21 \) cm, and \( 17.5 + 14 + 21 = 52.5 \) cm. The mistake to avoid is treating perimeter like area: the area of the enlarged triangle would be \( 1.75^2 = 3.0625 \) times the original, but the perimeter uses the plain factor \( 1.75 \) because it is measured in centimetres, not square centimetres.
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