Triangle a 7x + 7 5x - 4 4x + 2 Triangle b 2x -5 x + 3. x + 7 A. write an expression in simplest form for the perimeter of each triangle. B. write another expression in the simplest form that shows the difference between the perimeter of the larger triangle and the perimeter of the smaller triangle. C Find the perimeter for each triangle when x = 3
A. Perimeter of triangle a = 7x + 7 + 5x - 4 + 4x + 2 = 16x + 5
Perimeter of triangle b = 2x - 5 + x + 3 + x + 7 = 4x + 5
B. Difference in perimeter = (16x + 5) - (4x + 5) = 12x
C.
When x = 3,
Perimeter of triangle a = 16(3) + 5 = 53
Perimeter of triangle b = 4(3) + 5 = 17
A. To find the perimeter of a triangle, we add the lengths of all three sides.
Triangle a: 7x + 7 + 5x - 4 + 4x + 2
Simplifying, we can combine like terms:
= 7x + 5x + 4x + 7 - 4 + 2
= 16x + 5
Triangle b: 2x - 5 + x + 3 + x + 7
Simplifying, we can combine like terms:
= 2x + x + x - 5 + 3 + 7
= 4x + 5
B. The difference between the perimeter of the larger triangle (Triangle a) and the perimeter of the smaller triangle (Triangle b) is found by subtracting the smaller triangle's perimeter from the larger triangle's perimeter.
Perimeter difference: (16x + 5) - (4x + 5)
Simplifying, we can combine like terms:
= 16x - 4x + 5 - 5
= 12x
C. To find the perimeters of each triangle when x = 3, substitute x = 3 into the expressions we simplified in part A.
Perimeter of Triangle a: 16(3) + 5 = 53
Perimeter of Triangle b: 4(3) + 5 = 17