The lengths of the sides of a triangle are in the extended ratio 4:7:10. The perimeter of the triangle is 105 cm. What are the l

Question

vivado [14]

2 years ago

5

The lengths of the sides of a triangle are in the extended ratio 4:7:10. The perimeter of the triangle is 105 cm. What are the l

engths of the sides?

Mathematics

1 answer:

AlekseyPX · Answer 1 · 2022-12-16T10:59:09+03:00

<h3>Answer: 20 cm, 35 cm, and 50 cm</h3>

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Explanation:

The sides are in the ratio 4:7:10

This scales up to 4x:7x:10x showing that the sides are 4x, 7x and 10x. The variable x is some positive real number.

Add up the sides and set this equal to the given perimeter 105. Solve for x.

4x+7x+10x = 105

21x = 105

x = 105/21

x = 5

This value is then plugged into each side

4x = 4*5 = 20
7x = 7*5 = 35
10x = 10*5 = 50

The triangle has sides of 20 cm, 35 cm, and 50 cm.

Note how the ratio 20:35:50 reduces to 4:7:10 after dividing all three parts by the GCF 5. Also, we can see that 20+35+50 = 105 to fully confirm our answer.