Question

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

Answer 1

Answer:

$length=(\sqrt{40} )m,breadth=\frac{4\sqrt{40} }{5} m$

Step-by-step 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 $4:5=\frac{4}{5}$
• Let $l$ mean length and $b$ breadth, so the ratio $b:l=4:5,so,b:l=\frac{b}{l}=\frac{4}{5}$
• So if  $\frac{b}{l}=\frac{4}{5}$ then multiply both sides by $l$ and you get $b=\frac{4}{5} l$
• Now the equation for area is $area=length*breadth$ or $A=l*b$
• Since our breadth $b$ equals $\frac{4}{5} l$ then we substitute for the breadth
• So $A=l*(\frac{4}{5}*l)=\frac{4}{5}*l*l=\frac{4}{5} l^2$ so $A=\frac{4l^{2}}{5}$
• We know the Area is $32m^2$ so $32m^2=\frac{4l^{2}}{5}$  so we simplify
• $5*(32m^2)=5*(\frac{4*l^{2}}{5})\\ 160m^2=4*l^2\\ \frac{160m^{2}}{4}=\frac{4*l^{2}}{4} \\ 40m^2=l^2\\ l^2=40m^2\\ \sqrt{l^{2}} =\sqrt{40m^{2}} \\ l=(\sqrt{40})m$
• Now we find the breadth, since
• $b=\frac{4}{5}*l \\ b=\frac{4}{5}*(\sqrt{40} )m\\ b=\frac{4\sqrt{40} }{5} m$