Question

Look at the given triangles.

triangles
The blue triangle is a right triangle. The vertical leg is labeled with the expression 4 x plus 2. The horizontal leg is labeled with the expression 5 x minus 4. The hypotenuse is labeled with the expression 7 x plus 7.

The red triangle is a right triangle. The vertical leg is labeled with the expression x plus 3. The horizontal leg is labeled with the expression x plus 7. The hypotenuse is labeled with the expression 2 x minus 5.


a. Write an expression in simplest form 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 perimeter of the smaller triangle.

c. Find the perimeter for each triangle when x = 3

Answer 1

a. blue 16x + 5

a. red 4x + 5

b. 12x

c. blue 53

c. red 17

Explanation:

a.

The perimeter of a polygon is the sum of the lengths of the sides of the polygon.

Blue triangle:

side lengths: 4x + 2, 5x - 4, 7x + 7

perimeter = 4x + 2 + 5x - 4 + 7x + 7 = 16x + 5

Red triangle:

side lengths: x + 3, x + 7, 2x - 5

perimeter = x + 3 + x + 7 + 2x - 5 = 4x + 5

b.

We subtract the perimeter of the red triangle from the perimeter of the blue triangle.

16x + 5 - (4x + 5) =

= 16x + 5 - 4x - 5

= 12x

c.

Blue triangle:

perimeter = 16x + 5 = 16(3) + 5 = 48 + 5 = 53

Red triangle:

perimeter = 4x + 5 = 4(3) + 5 = 12 + 5 = 17