KJSEA 2025 Maths Q18 — Enlargement of a Photograph (Scale Factor)

KJSEA 2025 Grade 9 Geometry

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The Question

“A photograph was enlarged to twice its original size. The original photograph had a length of 16 cm. What was the new length of the enlarged photograph?”

1

Read the scale factor

The photograph is enlarged to twice its original size. In enlargement, the phrase 'twice the size' tells us the scale factor, which is the number that every length is multiplied by. Twice means a scale factor of two.

k=2k = 2
2

Write the enlargement rule

Under an enlargement, each length on the new image is the matching length on the original multiplied by the scale factor. So the new length equals the original length times the scale factor.

new length=k×original length\text{new length} = k \times \text{original length}
3

Substitute the known values

The original length is 16 cm and the scale factor is 2. Put these values into the rule so the multiplication is ready to work out.

new length=2×16 cm\text{new length} = 2 \times 16 \ \text{cm}
4

Do the multiplication

Multiply 16 by 2 to get the enlarged length. This gives the length of the photograph after it has been enlarged.

2×16=32 cm2 \times 16 = 32 \ \text{cm}

Final Result

The new length of the enlarged photograph is 32 cm (letter A).

Why this method works

Enlargement changes the size of a shape while keeping its proportions the same, and the scale factor is exactly the number that describes how many times bigger the new shape is. Because every length is stretched by the same factor, multiplying the original length by the scale factor gives the matching length on the enlarged image. Here a scale factor of 2 means the photograph becomes twice as long, so 16 cm doubles to 32 cm.

✓

Divide the new length by the original: 32 divided by 16 equals 2, which matches the scale factor, so the answer is consistent.