Question

The breadth and length of a rectangle are in the ratio 4:5 and its area is

32 sqm. What are the length and breadth?

Answer 1

`length=(√(40) )m,breadth=(4√(40) )/(5) m`

Explanation:

• So the ratio 4:5 relates the length and breadth
• Now the length is always longer that the breadth so 5 represents the length and 4 the breadth
• A ratio can be written as a fraction so
  `4:5=(4)/(5)`
• Let
  `l` mean length and
  `b` breadth, so the ratio
  `b:l=4:5,so,b:l=(b)/(l)=(4)/(5)`
• So if
  `(b)/(l)=(4)/(5)` then multiply both sides by
  `l` and you get
  `b=(4)/(5) l`
• Now the equation for area is
  `area=length*breadth` or
  `A=l*b`
• Since our breadth
  `b` equals
  `(4)/(5) l` then we substitute for the breadth
• So
  `A=l*((4)/(5)*l)=(4)/(5)*l*l=(4)/(5) l^2` so
  `A=(4l^(2))/(5)`
• We know the Area is
  `32m^2` so
  `32m^2=(4l^(2))/(5)` so we simplify
• 
  `5*(32m^2)=5*((4*l^(2))/(5))\\ 160m^2=4*l^2\\ (160m^(2))/(4)=(4*l^(2))/(4) \\ 40m^2=l^2\\ l^2=40m^2\\ \sqrt{l^(2)} =\sqrt{40m^(2)} \\ l=(√(40))m`
• Now we find the breadth, since
• 
  `b=(4)/(5)*l \\ b=(4)/(5)*(√(40) )m\\ b=(4√(40) )/(5) m`