Question 534572
Let x be the breadth of the unknown similar rectangle.
The length would be x+5.
Because they are similar, the ratios of corresponding sides are the same.
We could state the the ratio of lengths and the ratio of breadth is the same:
{{{(x+5)/28=x/18}}}
We eliminate pesky denominators by multiplying both sided times a common multiple of the denominators,
{{{254=4*7*9}}}
to get
{{{9(x+5)=14x}}} --> {{{9x+45=14x}}} --> {{{45=5x}}} --> {{{x=9}}}
Otherwise we could state the the ratio of length to breadth is the same for both rectangles:
{{{28/18=14/9}}} and {{{14/9=(x+5)/x}}}
Multiplying both sides by 9x would theoretically risk introducing x=0 as an extraneous solution, but x=0 would be rejected even if it was a solution of the equations. So we do it without worrying to get
{{{14x= 9(x+5)}}}
which is the same equation we solved above, of course.
The breadth of the mystery rectangle is 9 cm, and its length is
{{{9cm+5cm=14cm}}}