WILL GIVE BRAINLIEST 5 STARS AND THANKSAn automated machine takes any cardboard rectangle and cuts off a square whose side length is equal to the shorter side length of the rectangle. Peter had a rectangle and, using only the machine, got out of it 2 large squares, 3 medium squares, and 5 small squares whose side length is 10 cm. What were the dimensions of Peter's rectangle?

Dimensions:

x = 130 cm

y = 10 cm

Step-by-step explanation:

Let´s call "x" and "d" sides of the cardboard rectangle x > y

then we have to cut along x three pieces of y length to get three squares of sides "y".

We have two squares of side y, the third one we cut in half and get two rectangles with sides y  and y/2, we cut to get 4 squares with sides y/2 then so far we have

2 large squares     ( side y )

4 medium squares (side y/2)  we just need three

We need to cut the available square side y/2  in 4 to get y/4 squares

Finally, we need y/4 length to get the fifth  y/4 square

Then dimensions of the cardboard

x       and   y

We cut 3 times at  "y" length and  need additional 10 cm

Then the side y/4 is equal to 10 cm then y = 40 cm

and  x = 3*y + y/4

x = 3*40 + 10 = 130 cm

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb