The perimeter of a triangle is 82 centimeters. If two sides equally long and the third side is 10 centimeters longer than the others, find the lengths of the three sides.

Question

We also have to find if it is centimeters or square centimeters.

Answer 1

Hello, Sun Hee,

Let's set x equal to the length of the two sides having the same length. The third side would have length x + 10. The sum of all three is the perimeter, 82 centimeters (cm). So add the three sides and set it equal to 82 cm.

x + x + x + 10 = 82 cm

3x = 72cm

x = 24cm

Therefore two sides are 24cm and the third is 34 cm. That adds to 82 cm. This is not area (cm²⁾, just length, cm. The three units are simply added - there is no multiplication that would produce cm².

Bob

Answer 2

From the problem we know the perimeter is 82 or P = 82 cm. Lets assume these are all in cm, since they are all measures of length

Let's call the sides of the triangle a, b, and c. Then we know the perimeter equals the sum of a, b, and c.

P = a + b + c

82 = a + b + c

Two sides are equal, so let's say a = b. we can replace the b in the equation with an a:

82 = a + a + c

The third side is c, which is 10 longer than the other two. That means c = a + 10, so we can replace the c with (a + 10):

82 = a + a + (a + 10)

Now that we only have one variable, we can solve for a:

82 = 3a + 10

72 = 3a

a = 24

We know a = b, so b = 24 too.

We also know c = a + 10, so we now have all three sides:

c = a + 10

c = 24 + 10

c = 34

a = 24 cm

b = 24 cm

c = 34 cm

We can check our work by adding all the sides together (24 + 24 + 34 = 82) and confirming that one side is 10 cm longer than the other two. The measures are all lengths, so the units should be cm. cm² is a unit of area, so it wouldn't make sense here unless we were multiplying one side by another.

Answer 3

3x+10 = 82

3x=72

x = 72/3 = 24 cm for 2 sides

x+1 = 34 cm for the 3rd side

The perimeter and sides are in centimeters

The Area is in square centimeters =17sqr287) = almost 289 square cm = 289 cm^2

A=hb/2=height times base divided by 2 = (sqr287)34/2 = 27sqr287 cm^2