Best Answer

There are 25. For an isosceles triangle with sides a, b & c, with a = c. The sides are all positive whole numbers. The perimeter = a + b + c = 2a + b. Ans 2a must be greater than b, or it won't be a closed figure. If 2a = b, it will be a just a line segment, not a triangle.

So start at 2a = b, which gives b = 49.5, and a = c = 24.75. The largest value of b that is valid will be: b = 49 [a whole number], and 2a = 99-49 = 50, so a = c = 25.

The values of b will have to be odd, since 2a will always be even, and they must add up to an odd number [99]. So the valid values of b are {1,3,5,...45,47,49}, which is 2n-1, with n = 1..25.

The sides of the triangle will be: {(1,49,49); (3,48,48); (5,47,47);...; (47,26,26); (49,25,25)}

Q: How many isosceles triangles exist with a perimeter of 99 inches and side lengths that are positive whole numbers?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

It is the sum of the lengths of its sides.

The triangles have the same side lengths.

Pyramids are not isosceles triangles but their triangular faces can form the image of an isosceles triangle if they have two sides of equal lengths and a base of a different length.

Add the lengths of the three individual sides.

Yes. With suitable choice of lengths a triangle can have any area.

Related questions

Isosceles triangles are triangles in which two of the three sides have different lengths.

It is the sum of the lengths of its sides.

The triangles have the same side lengths.

Scalene triangles those triangles in which all the sides are of different lengths, but in isosceles triangles two sides of the triangle are equal in length. Therefore, no scalene triangle can ever be isosceles.

Pyramids are not isosceles triangles but their triangular faces can form the image of an isosceles triangle if they have two sides of equal lengths and a base of a different length.

Lengths of: equal side+equal side+base = perimeter

Add the lengths of the three individual sides.

24cm each

No, scalene triangles, which have sides of different lengths, have none. Isosceles triangles, with only two sides the same, only have one.

No, all isosceles triangles are not equilateral triangles. An isosceles triangle is a triangle that has two sides of equal length. An equilateral triangle is a triangle that has all three sides of equal length. Therefore, it is possible for a triangle to be isosceles but not equilateral. For example, a triangle with sides of lengths 3, 3, and 4 is an isosceles triangle, but it is not an equilateral triangle because all its sides do not have the same length. On the other hand, all equilateral triangles are also isosceles triangles because they have two sides of equal length. My recommendation ʜᴛᴛᴘꜱ://ᴡᴡᴡ.ᴅɪɢɪꜱᴛᴏʀᴇ24.ᴄᴏᴍ/ʀᴇᴅɪʀ/372576/ꜱᴀɪᴋɪʀᴀɴ21ᴍ/

Yes. With suitable choice of lengths a triangle can have any area.

There is only one equilateral triangle with a perimeter of 60 units. Its side lengths are integers.