Question

The measure of the perimeter of a triangle is 10a+3b+12. It is known that two of the sides of the triangle have measures of 3a+8 and 5a+b. If x=1cm, find the length of the third side in cm.

Answer 1

To find the length of the third side of the triangle, the equation combining the lengths of all three sides was used and simplified, revealing the third side to be 2a + 2b + 4. With x=1cm, the length of the third side is determined to be 8 cm.

Step-by-step explanation:

The measure of the perimeter of a triangle is given as 10a+3b+12. This perimeter is the sum of the lengths of all three sides of the triangle. Two of the sides are already provided with lengths of 3a+8 and 5a+b. To find the length of the third side, we can set up the equation:

3a + 8 + 5a + b + third side = 10a + 3b + 12

Combining like terms on the left-hand side gives us:

8a + b + 8 + third side = 10a + 3b + 12

Now, we isolate the third side:

third side = 10a + 3b + 12 - (8a + b + 8)

This simplifies to:

third side = 2a + 2b + 4

Substituting x=1cm into the equation:

third side = 2(1) + 2(1) + 4 = 2 + 2 + 4 = 8 cm

Therefore, the length of the third side of the triangle is 8 cm.