Question

The perimeter of right triangle RST is equal to the perimeter of isosceles triangle XYZ. The lengths of the legs of the right triangle are 6 and 8. If the length of each side of the isosceles triangle is an integer, what is the greatest possible length for one of the sides of the isosceles triangle XYZ?

Answer 1

The lengths of the legs are 6, 8, by pythagoras the hypotenuse is 10 for a total of 24

Answer 2

Is the pythagoras theorm \[a ^{2}+b ^{2}\]

Answer 3

\(a^2+b^2=c^2\) and so
\[6^2+8^2=c^2\] tells you \(c=10\)

Answer 4

So the type of triangle does not matter?

Answer 5

as for the isosceles triangle, i guess the sides could be 11, 11, and 2
not sure if you can get a longer side

Answer 6

no it matter
that is for a right triangle

Answer 7

For the isosceles triangle then it one of the side has to be 10?
The problem had options

Answer 8

How about 22 1 and 1
It asks for length of longest side

Answer 9

i think two sides could be 11, the third side 2

Answer 10

A.) 10
B.) 11
C.) 14
D.) 16
E.) 22

Answer 11

I'd say E

Answer 12

there is no triangle with two sides 1, and one side 22

Answer 13

try to draw it and you will see why

Answer 14

but there is a 11, 11, 2, triangle

Answer 15

Geez yes - I was interested in the mathematical solution. I neglected the geometry.

Answer 16

Geometry is all logic haha

Answer 17

Yes the Triangle Inequality Theorem
Any side of a triangle must be:
less than the sum of the other 2 sides and
greater than the difference of the other 2 sides.

Answer 18

So which answer is best 10 or 11?

Answer 19

I'd say satellite73 had the correct solution
11

Answer 20

Alright, Thank You Both! c:

Answer 21

u r welcome
(and I'd better slow down in my anxiety to find the "correct" solution)