Question

Two similar cardboards have areas of 24cm² and 150cm². If the length of the bigger one is 10cm ,what is the length of the smaller one,?

Answer 1

4 cm

Explanation:

You want the length of the smaller of two similar pieces of cardboard when the larger has an area of 150 cm² and a length of 10 cm, while the smaller has an area of 24 cm².

Scale factor

The scale factor for lengths is the square root of the scale factor for areas. It will be ...

√(24/150) = 0.4 . . . . . . = smaller / larger

The smaller cardboard has a length of ...

0.4 × 10 cm = 4 cm

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Additional comment

Sometimes folks like to write this as a proportion:

`\frac{\text{smaller length}}{\text{larger length}}=\sqrt{\frac{\text{smaller area}}{\text{larger area}}}`

Solving this for "smaller length" gives the expressions we used above:

smaller length = (larger length) × √(smaller area/larger area)