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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?

User Angelo
by
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1 Answer

2 votes

Answer:


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
User Bart Platak
by
7.8k points

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