Each dimension of a right triangle with legs of length 6 cm and 8 cm and a hypotenuse of length 10 cm is multiplied by 1/2 to form a similar right triangle. How is the ratio of perimeters related to the ratio of corresponding sides? How is the ratio of areas related to the ratio of corresponding sides?

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Mathematics

19 July, 07:59

Each dimension of a right triangle with legs of length 6 cm and 8 cm and a hypotenuse of length 10 cm is multiplied by 1/2 to form a similar right triangle. How is the ratio of perimeters related to the ratio of corresponding sides? How is the ratio of areas related to the ratio of corresponding sides?

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Marianna Evans · Answer 1

Perimeter of original triangle: 6+8+10=24 cm

Perimeter of new triangle: 3+4+5=12 cm (You get 3, 4, and 5 from dividing 6, 8. and 10 by 2.)

Ratio of original to new is 24 to 12, simplified to 2 to 1.

The ratio of the perimeter is the ratio of the corresponding sides, as the original measurements are two times the length of the new measurements.

Area of original triangle: (6x8) / 2=24 cm^2

Area of new triangle: (3x4) / 2=6 cm^2

Ratio of original to new is 24 to 6, simplified to 4 to 1.