Triangle inequality

2012-10-10 4:26 am

1）If the lenghts of two sides od an triangle are 3cm and 8cm.what is the perimeter of the triangle？
2）the perimeter of an isosceles triangle is 18cm .lf the length of one side is 4cm ，find the lengths of the other two sides？

回答 (1)

micatkie

2012-10-10 7:13 am

✔ 最佳答案

1)
Let x cm be the length of the third side, and p cm be the perimeter.

The sum of any two shorter sides of a triangle must be greater than the longestside.

If the longest side is 8 cm :
3 + x > 8
x > 5

If the longest side is p cm :
3 + 8 > x
x < 11

5 < x < 11
(5 + 3 + 8) < (x + 3 + 8) < 11 + 3 + 8
16 < p < 22
16cm < perimeter < 22 cm

2)
If the length of one of the other two sides is 4 cm :
Length of the third side
= 18 - (4 + 4) cm
= 10 cm

If the lengths of the other two sides are equal :
Length of each of the other two sides
= (18 - 4)/2 cm
= 7 cm

The other two sides are 4 cm and 10 cm, or 7 cm and 7 cm.

參考: micatkie

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