SOLUTION: I've tried to help my son but am clueless. two isosceles triangles have the same base length. the legs of one of the triangles are twice as long as the legs of the other. find t

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Question 13788: I've tried to help my son but am clueless.
two isosceles triangles have the same base length. the legs of one of the triangles are twice as long as the legs of the other. find the lengths of the sides of the triangles if their perimeters are 23cm and 41cm.
Can you please help?
Thanks
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, an isosceles triangle has two equal sides and a base.
Let x = the length of the base of each isosceles triangle and y = the length of each side of the smaller triangle. So, the sides of the larger triangle are each 2y. Now you can set up the system of equations relating the sum of the sides of each triangle to their respective perimeters.
1) x+%2B+2y+=+23 and
2) x+%2B+4y+=+41 Subtract equation 1) from equation 2)
3) 2y+=+18 Divide both sides by 2.
y+=+9
The length of each side of the smaller isosceles triangle is 9 cm.
The length of each side of the larger isosceles triangle is 2 X 9 = 18 cm.
Incidentally, the length of the base of each triangle is:
23+-+2y+=+23+-+18 = 5 cm.