Adam has sticks of the following lengths: (3x + 4) cm, (2x + 10) cm, and (x + 12) cm. He puts all three sticks together to make an isosceles triangle. Calculate the three possible values of x.

option I (3x+4)cm =(2x+10)cm 3x-2x=6 x=6 Option II (3x+4)= (x+12) 3x-x=12-4 2x=8 x=4 Option III (2x+10)= (x+12) 2x-x=12-10 x=2

Answered by tmacar | 2024-06-10

Isosceles triangles, are triangles where two of the lengths are the same so we can say that: 1. (3x+4)=(2x+10) 2. (3x+4)=(x+12) 3. (2x+10)=(x+12) One of these must be true. Solve as simultaneous equations.

x=6
x=4
x=2

Answered by cjbuckleyuk | 2024-06-10

The three possible values of x that make the triangle isosceles are 6 , 4 , and 2 . Each pair of stick lengths can be set equal to find these values. All three value pairs also satisfy the triangle inequality.
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Answered by tmacar | 2024-10-30