Friday

August 29, 2014

August 29, 2014

Posted by **Anonymous** on Tuesday, August 28, 2012 at 3:15pm.

The sides of a triangle are 5 cm, x cm, and y cm.

List possible values for x and y.

- geometry -
**Steve**, Tuesday, August 28, 2012 at 4:41pmsince any side is less than the sum of the other two sides,

x+y > 5 (duh)

x+5 > y

y+5 > x

lots of possible solutions:

5,11,9

5,13,13

and more

- geometry -
**Reiny**, Tuesday, August 28, 2012 at 5:02pmvalues of x could be 11, 12, or 13

values of y could be 9, 10, 11, 12 or 13

now overthinking the problem:

To have a triangle:

1. x+y > 5

2. x+5 > y ----> x-y > -5 or y-x < 5

3. y+5 > x ----> y-x > -5

from #2 and #2 we can see that

-5 < y-x < 5

so make 3 columns

5_x__y_(y-x)

5 11 9

5 11 10

5 11 11

5 11 12

5 11 13

5 12 9

5 12 10

..

5 12 13

5 13 9

..

5 13 13

in short, the x could be 11, 12 or 13

the y could be 9, 10, 11, 12, or 13

so the number of triangles for sides labeled x , y and 5 is 3(5) or 15

However, triangles 5 , 12, 13 and 5, 13, 12 are the same triangle

there are 3 such duplicated pairs, so

the actual number of triangles possible is 15-3 = 12

**Related Questions**

Geometry - 1. The sides of a triangle have lenghts x, x+4, and 20. Specify those...

Geometry - determine all possible values of x if 2x+10, 20-x, and 3(x-15) are ...

geometry - the sides of an acute triangle are x, 35, and 37, where x is the ...

geometry - The sides of an acute triangle are x, 35, and 37, where x is the ...

Integers - Suppose a1, a2, . . . , an is a list of n numbers with the following ...

Geometry Help!!!!!!!!!! - If the sides of a triangle have measurements 3x + 4 , ...

Algebra - Need help with these-- 21. Find the possible values of a, of the ...

Mathematics - How do i post the answer hence i don't the answer .In geometry.an ...

Geometry - ABC is an obtuse triangle with m<A=21 and <C is acute. a)What ...

geometry - The measure of an exterior angle of an isosceles triangle is x ...