The perimeter of a triangle is 81 cm if two sides are equally long and the third side is 6 cm longer than the others find the lengths of the three sides

Answer 1

This is a a combination of geometry and algebra. The goal is set up an expression to solve for the sides.

Designate the first side length as x. Since there are two sides that are equal, there are two x's. The third side is 6 cm more than x.

The expression now reads:

Perimeter = P = 81cm = x+x+(x+6)

This could also be written as: 2x+(x+6)

Solving gives us:

3x+6=81

3x=75

x=25

So two sides are 25cm long, and the third is 31 cm long

Answer 2

Hi, Em,

Put the words into formulas. Let P = the perimeter. Let X, Y and Z be the three sides (line 2) equal to 81 cm. We know two sides are the same, so let's substitute X for Y (line 3), We also know the third line is 6cm longer than the other two (line 4). Substitute line 4 into line 3 to get line 5. We are left with only X's for the unknowns, so sum, rearrange, and find X. Then use that to find Y (the same) and Z (6cm longer) in line 4. Check to be sure all three add to 81cm, and then we're done. Fun!

Bob

Answer 3

Let's set up an equation to represent the question.

We have two sides that are equally, we'll call each one x,

The third side is 6 cm less than the other side, well we said the "other side" is equal to x. So the third side is equal to x - 6.

Now we think about the definition of a perimeter: the distance of the outline of a shape, or in this case the sum of the three sides

side1 + side2 + side3 = 81

or

x + x + (x-6) = 81

Now we solve for x

3x - 6 =81

3x = 87

x = 29

so side1 = x = 29

side2 = x = 29

side3 = x-6 = 23

Finally lets check our work

side1 + side2 + side3 = 81

29 + 29 + 23 = 81

81 = 81