finding the area of a picture frame

Question

14) A picture frame has a total length and breadth of 20cm and 10cm. The frame has a width of x cm.

a) find the rule for the area (A cm^2) of the picture inside.

14, a has already been figured out = A = (10-2x)(20-2x)

b)what are the minimum and maximum values of x?

Hi I am stuck with question 14, b. please explain with detail and please don't make it look like codes as its a little hard to read. I'd appreciate it if it is handwritten, but if not then its fine. thank you!

Answer 1

x>0

and length and width of the picture must be greater than zero

10-2x>0

10>2x

5>x

x<5

0<x<5

20-2x>0

10-x>0

10>x

x<10

0<x<5<10 the last part is unnecessary, or redundant

minimum x value is 0 cm

maximum x value is 5 cm

0 cm < x < 5 cm