# algebra

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.

1. 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

posted by Reiny
2. 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

posted by anonymous
3. 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

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

posted by anonymous
5. 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...????????

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

posted by Reiny
7. 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?

posted by anonymous
8. i don't know the answer

posted by Anonymous

## Similar Questions

1. ### geometry

The perimeter of an isosceles triangle is 37 in. The lengths of the two equal legs are 6 in. less than 3 times the length of the base. Find the lengths of the three sides. 37=2L+2W W=3W-6 do i have this equation wrote right when i
2. ### Math

In a diagram of an 2 isosceles triangles, where ABC is a big triangle and a ADE, is just inside the top portion of ABC. Isosceles triangle ABC is similar to a isosceles triangle ADE what is the length of DE, which is the base part
3. ### math

The base of an isosceles triangle is four less than the sum of the lengths of the legs. If the perimeter of the triangle is 44, find the length of the three sides of the triangle.[ Only an algebraic solution will be accepted ]
4. ### Geometry

the legs of an isosceles triangle have lengths 2x+4 and x-8 the base has length 5x-2 whats the lenght of base
5. ### geometry

The perimeter of an isosceles triangle is 37 in. The lengths of the two equal legs are 6 in. less than 3 times the length of the base. Find the lengths of the three sides. 37=2L+2W W=3W-6 do i have this equation wrote right when i
6. ### Math (Geometry)

The perimeter of right triangle ABC is equal to the perimeter of isosceles triangle DEF. 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
7. ### Math

If all of the following triangles have the same perimeter, which has the greater area? a) a right triangle with legs of equal lengths b) an equilateral triangle, c) An obtuse triangle d) a triangle whose sides are all different
8. ### geometry

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
9. ### Math

Two isosceles triangles have perimeters of 8 and 15 centimeters, respectively. They have the same base length, but the legs (the non base sides) of the larger triangle are twice as long as the legs of the smaller triangle. For
10. ### math

the legs of an isosceles triangle have lengths x+1 and -x+7. the base has length 3x-3. what is the length of the base? a. 6 b. cannot be determined c. 4 d. 3

More Similar Questions