The legs of a right triangle XYZ are 5 cm and 12 cm. Triangle XYZ is dilated to triangle X'Y'Z' by a scale factor of 2/3. What is the area of triangle X'Y'Z'?

Question

Mathematics

Tatum Fowler

24 January, 13:46

The legs of a right triangle XYZ are 5 cm and 12 cm. Triangle XYZ is dilated to triangle X'Y'Z' by a scale factor of 2/3. What is the area of triangle X'Y'Z'?

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Booth · Answer 1

Assuming that the base is 5 cm and the height is 12 cm, so by dilating the legs by a scale factor of 2/3, the new dimensions are:

base = 5 cm * (2 / 3) = 10/3 cm

height = 12 cm * (2 / 3) = 8 cm

So the area of a right triangle is calculated using the formula:

A = b h / 2

A = (10/3) * 8 / 2

A = 13.33 cm^2