# algebra

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The base of an isosceles triangle and one of its legs have lengths that have consecutive integers. The leg is longer than the base. The perimeter of the triangle is 20. Find the length of each side of the triangle.

• algebra - ,

Let the base be x units long.
"Consecutive integers" are one apart, so if the first one is x then the next one must be x+1.

So the other two sides must be x+1 each.

Since perimeter is the sum of the 3 sides...
x + x+1 x + x+1 = 20
3x + 2 = 20
3x=18
x=6

So the base is 6 and each of the other two sides is 7

check: 6 and 7 are consecutive integers
6+7+7 = 20

• algebra - ,

x + x+1 x + x+1 = 20
In the above, where did you get the 1x from? This is what I came out with:
x+x+x+1=20

• algebra - ,

It was clearly a typo
looking at the line that follows should have made it obvious.

this is what it should have been putting the sides in brackets

(x) + (x+1) + (x+1) = 20

• algebra - ,

ok I get it. I got x= 6 now i can go from there. Thanjs much for all your help!

• algebra - ,

Would the let statements go like this then:
Let x= 1st C.I.= 6
Let x+1= 2nd C.I.= 7
Let x+1= 3rd C.I.= 7
b/c the second and 3rd aren't C.i.s, so...????????

• algebra - ,

You said the triangle was isosceles, so two of its sides have to be the same.

• algebra - ,

yeah, but how do i convey that in the let statements? 7=7, so they aren't consec. integers, right? if so, what do i put instead?

• algebra - ,