Look at the given triangles.
4x+1 5x+5 7x-2
2x+2 6x+2 X+6
A)Write an expression for the perimeter of each triangle.
B)Write another expression in simplest form that shows the difference between the perimeter of the larger triangle and the smaller triangle.
C)Find the perimeter for each triangle when x = 2.
A) The perimeter of a triangle is the sum of the lengths of its three sides. Therefore, the perimeter of the first triangle is:
4x+1 + 5x+5 + 7x-2 = 16x + 4
And the perimeter of the second triangle is:
2x+2 + 6x+2 + x+6 = 9x + 10
B) To find the difference between the perimeters, we subtract the smaller from the larger:
(9x + 10) - (16x + 4) = -7x + 6
C) To find the perimeter of each triangle when x = 2, we simply substitute 2 for x in the expressions we found in part A:
Perimeter of first triangle: 16(2) + 4 = 36
Perimeter of second triangle: 9(2) + 10 = 28
Let's solve the problem step by step:
A) To find the perimeter of each triangle, we add up the lengths of all the sides of the triangle.
Triangle 1: Side lengths are 4x + 1, 5x + 5, and 7x - 2.
Perimeter of Triangle 1 = (4x + 1) + (5x + 5) + (7x - 2)
= 4x + 1 + 5x + 5 + 7x - 2
= 16x + 4
Triangle 2: Side lengths are 2x + 2, 6x + 2, and x + 6.
Perimeter of Triangle 2 = (2x + 2) + (6x + 2) + (x + 6)
= 2x + 2 + 6x + 2 + x + 6
= 9x + 10
So, the expressions for the perimeter of each triangle are:
Perimeter of Triangle 1 = 16x + 4
Perimeter of Triangle 2 = 9x + 10
B) To find the difference between the perimeters of the larger triangle and the smaller triangle, we subtract the perimeter of the smaller triangle from the perimeter of the larger triangle.
Difference = (Perimeter of Triangle 1) - (Perimeter of Triangle 2)
= (16x + 4) - (9x + 10)
= 16x - 9x + 4 - 10
= 7x - 6
So, the expression for the difference between the perimeters of the larger triangle and the smaller triangle is:
Difference = 7x - 6
C) To find the perimeter of each triangle when x = 2, we substitute x = 2 into the expressions we found earlier.
Perimeter of Triangle 1 when x = 2:
Perimeter of Triangle 1 = 16x + 4
= 16(2) + 4
= 32 + 4
= 36
Perimeter of Triangle 2 when x = 2:
Perimeter of Triangle 2 = 9x + 10
= 9(2) + 10
= 18 + 10
= 28
So, the perimeter of Triangle 1 when x = 2 is 36, and the perimeter of Triangle 2 when x = 2 is 28.