The ratio of length to width is 3/2. Let's set up equations of ratios using first the 25 cm length of the paper and then the 20 cm width:
3 25 cm
--- = ----------
2 x
Solving for x, 3x = 50 cm, and x =16 2/3 cm. This is possible, since 16 2/3 is less than the paper width 20 cm.
3 20 cm
--- = -----------
2 x
Solving for x: 3x = 40 cm; x = 40/3 cm, or x= 13 1/3 cm. This is possible, but does not make maximum use of the 20 by 30 cm paper.
Answer: the largest flag Jake can draw on the paper given is 20 cm (length) by 16 2/3 cm.
Hypotenuse of the right triangle: h=sqrt(4^2+6^2)
h=sqrt(16+36)
h=sqrt(52)
h=sqrt(4*13)
h=sqrt(4) sqrt(13)
h=2 sqrt(13)
Total Area: T.A.=2*(4*6/2)+[4+6+2 sqrt(13)] (8)
T.A.=2*(12)+[10+2 sqrt(13)](8)
T.A.=24+(10)(8)+[2 sqrt(13)](8)
T.A.=24+80+16 sqrt(13)
T.A.=104+16 sqrt(13)
Answer:
( 104+16 sqrt(13) )
3364
= 2^2 * 29^2
So
√3364 = √(2^2 * 29^2) = 2 * 29 = 58