The ancient Egyptians had a neat way to construct right angles. They would make a long rope with knots to make 121212 equal sections. When they stretched the rope into the triangle shown below, they always got a right angle. This was useful when planning the pyramids, for example. If we apply the Pythagorean Theorem to the Egyptian knots we can see that 3^2 + 4^2 = 5^23 2 +4 2 =5 2 3, squared, plus, 4, squared, equals, 5, squared. Which of the sets of three numbers listed would also let you form a right angle in this way? Choose all answers that apply: Choose all answers that apply: (Choice A) A \text{\{36, 85, 77\}}{36, 85, 77}start text, left brace, 36, comma, space, 85, comma, space, 77, right brace, end text (Choice B) B \text{\{24, 24, 30\}}{24, 24, 30}start text, left brace, 24, comma, space, 24, comma, space, 30, right brace, end text (Choice C) C \text{\{2, 5, 9\}}{2, 5, 9}start text, left brace, 2, comma, space, 5, comma, space, 9, right brace, end text (Choice D) D \text{\{5, 12, 13\}}{5, 12, 13}

Part a what is the area of triangle i? show your calculation. part b triangles i and ii are congruent (of the same size and shape). what is the total area of triangles i and ii? show your calculation. part c what is the area of rectangle i? show your calculation. part d what is the area of rectangle ii? show your calculation. part e rectangles i and iii have the same size and shape. what is the total area of rectangles i and iii? show your calculation. part f what is the total area of all the rectangles? show your calculation. part g what areas do you need to know to find the surface area of the prism? part h what is the surface area of the prism? show your calculation. part i read this statement: “if you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” is this statement true or false? why? part j read this statement: “if you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” is this statement true or false? why?

Afactory adds 3 red drops and 2 blue drops of coloring to white paint to make each pint of purple paint. the factory will make 50 gallons of the purple paint.how many drops of red and blue coloring will the factory need in the 50 gallon batch of purple paint.

Asif spent $745.10 on 13 new file cabinets for his office. small file cabinets cost $43.50 and large file cabinets cost $65.95. write and solve a system of equations to find the number of small cabinets and large cabinets he purchased. determine if each statement is true or false. 1. he purchased 5 small cabinets. true or false 2. he purchased 7 large cabinets. true or false 3. he spent $527.60 on large cabinets. true or false