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Mathematics

Grade9

Easy

Question

The scale factor of two similar hexagons is 5: 8. If the perimeter of the smaller hexagon is 45 inches, then find the perimeter of the larger hexagon.

72 inches
27 inches
64 inches
84 inches

hint Hint:

If the ratio is the same for all corresponding sides, then this is called the scale factor and the polygons are similar.

The correct answer is: 72 inches

If ratios of corresponding sides are equal then ratio of perimeter are also equal. The ratio of the perimeter is equal to the scale factor. Let the perimeter of the larger hexagon be x.
$fraction numerator 5 over denominator 8 end fraction equals fraction numerator 45 over denominator x end fraction$
$5 x equals 8 cross times 45$
$x equals fraction numerator 8 cross times 45 over denominator 5 end fraction$
$x equals fraction numerator 360 over denominator 5 end fraction$
$x equals 72$
Therefore, the perimeter of the larger hexagon is 72.

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