Posted by **tee** on Monday, November 4, 2013 at 1:20am.

the perimeter of a triangle is 42 inches. three times the length of the longest side minus the length of the shortest side is 49 inches. the sum of the length of the longest side and twice the sum of both the other side lengths is 65 inches. find the side lengths

- math -
**Bosnian**, Monday, November 4, 2013 at 3:06am
a = the length of the shortest side

b = the length of the middle side

c = the length of the longest side

P = the perimeter

The perimeter of a triangle is 42 inches.

P = a + b + c

a + b + c = 42 Subtract c to both sides

a + b + c - c = 42 - c

a + b = 42 - c

The sum of the length of the longest side and twice the sum of both the other side lengths is 65 inches.

c + 2 ( a + b ) = 65

c + 2 ( 42 - c ) = 65

c + 2 * 42 - 2 * c = 65

c + 84 - 2 c = 65

- c + 84 = 65 Add c to both sides

- c + 84 + c = 65 + c

84 = 65 + c Subtract 65 to both sides

84 - 65 = 65 + c - c

19 = c

c = 19 in

Three times the length of the longest side minus the length of the shortest side is 49 inches.

3 c - a = 49 Add a to both sides

3 c - a + a = 49 + a

3 c = 49 + a Subtract 49 to both sides

3 c - 49 = 49 + a - 49

3 c - 49 = a

a = 3 c - 49

a = 3 * 19 - 49

a = 57 - 49 = 8

a = 8 in

a + b + c = 42

8 + b + 19 = 42

27 + b = 42 Subtract 27 to both sides

27 + b - 27 = 42 - 27

b = 15 in

The side lengths:

a = 8 in

b = 15 in

c = 19 in

- math -
**Bosnian**, Monday, November 4, 2013 at 3:08am
84 = 65 + c Subtract 65 to both sides

84 - 65 = 65 + c - 65

19 = c

c = 19 in

## Answer this Question

## Related Questions

- geometry - The perimeter of a triangle is equal to 12 inches. The length of the ...
- Algebra 1 - The perimeter of a triangle is 20 inches. The longest side is 4 ...
- algebra - The perimeter of a triangle is 57in. The longest side is 13in. longer ...
- geometry - the perimeter of a triangle is 59 inches. the longest side is 11 ...
- math - The longest side of a triangle is six more units that the shortest side. ...
- pre- algebra - The perimeter of a triangle is 24 cm. One side is 2 cm longer ...
- Math - The perimeter of an equlateral triangle is 45 inches. A rectangle whose ...
- Algebra - One side of a triangle is 3 inches shorter than twice the length of ...
- math - the perimeter of a triangle is 79.75 inches. the second side of the ...
- Math - The two shortest sides of a right triangle are 10 inches and 24 inches ...

More Related Questions