Question

A seamstress is making a decorative pillow and wants to see lace around the trim. The pillow is in the shape of a triangle with vertice (7,7)(10,3)(7,3). How many inches of lace will she need if each unit on the grid is one inch?

Answer 1

To find the amount of lace needed for the pillow trim, calculate the lengths of the triangle sides using the distance formula and the differences in coordinates. The seamstress will need a total of 12 inches of lace.

Step-by-step explanation:

The question asked is about determining the amount of lace a seamstress would need to trim a decorative pillow shaped as a triangle with specific vertices on a grid. The vertices given are (7,7), (10,3), and (7,3). Since the grid units represent inches, we need to find the lengths of the sides of the triangle to calculate the total amount of lace needed.

The first side is from (7,7) to (10,3), which can be found using the distance formula: = √((₂ - ₁)² + (₂ - ₁)²) = √((10 - 7)² + (3 - 7)²) = √(9 + 16) = √25 = 5 inches.

The second side is a vertical line from (7,3) to (7,7), which is simply the difference in the y-coordinates, so the length is |3 - 7| = 4 inches.

The third side is a horizontal line from (10,3) to (7,3), which is the difference in the x-coordinates, so the length is |10 - 7| = 3 inches.

Adding up the lengths of all three sides, the seamstress would need 5 + 4 + 3 = 12 inches of lace to trim the pillow.

Answer 2

I think it will be 8 1/3 inches.
(7,7) and (7,3) are 4 units apart
7-3 = 4
7-7 = 0
(7,3) and (10,3) are 3 units away
3-3 = 0; 10-7 = 3
(7,7) and (10,3) are 4/3 units away or 1 and 1/3
7-3 = 4
7-10 =-3
Then, take the absolute value because you can't have negative inches of lace, you get 4/3 or 1 1/3.
Add them all together for perimiter:
4+3+1 1/3 = 8 1/3 inches of lace

Hope this helps!