what is the max number of isosceles right triangles whose legs are 3 inches long that can be cut from a rectangular sheet of paper measuring 14 x 10 inches.

a. 12

b. 15

c. 24

d. 30

e. 31

so 1. how do you do this problem?

2. why can't i compare areas? like the way i did it below....

my way: i compared areas: area of rectangular sheet/area of triangle

140/(.5) (3)(3)=140 (2/9) = approximately 15 x 2=30 this is under approximation so I choose E as the answer

answer to problem: C: 24

instead, kaplan compared sides 14/3 =4 and 10/3= 3 4x 3 =12 so if you double this you get 24 if you think about 2 isosceles =1 square.

I'd do it just like how kaplan did. if you put two isosceles triangles together against their hypotenuse, it'll give you 3x3 square. you can fit 4 squares on a row and 3 squares on a column so you'll make 12 squares which is equal to 24 triangles.

You can't compare areas because after you cut out the triangles there will be paper left that is 2x10 and 14x1 rectangle (they have intersection where they meet so it's technically not 34 but number still works, it would be 2x9 and 14x1 or 2x10 and 12x1 = 32), which adds up to 34 and theoretically capable of making 3 more squares (9x3) = 6 more triangles. But that can't happen because triangle must have 3 inches by 3 inches but they only have 2 inches on one side and 1 inch on one side of the rectangle.

I'm sorry my explanation is very confusing

it'll be easier if you visualize it

Edit: Sorry for my poor drawing but it'll help you probably. The side of the rectangle isn't big enough to construct triangles