For this case we have the following data:
Area of the rectangle, [tex]A = 125[/tex]
Relationship of the sides 5: 3
By definition, the area of a rectangle is given by:
[tex]A = a * b[/tex]
Where
- b: it is the side of least length.
If the sides have a 5: 3 ratio, it means:
[tex]\frac{a}{b}=\frac{5}{3}[/tex]
[tex]a=\frac{5}{3}b[/tex]
Substituting in the formula of the area, we have:
[tex]125 =a * b\\[/tex]
[tex]125=\frac{5}{3}b*b[/tex]
Clearing b:
[tex]3 * 125 = 5 * b ^ 2[/tex]
[tex]\frac{375}{5}= b ^ 2[/tex]
[tex]75 = b ^ 2[/tex]
[tex]b =\sqrt{75}b = 8.7[/tex] units
Substituting and clearing:
[tex]125 = a * 8.7[/tex]
[tex]a =\frac{125}{8.7}[/tex]
[tex]a = 14.4[/tex]units
So, the sides are:
[tex]a = 14.4[/tex]units
[tex]b = 8.7[/tex]units
Answer:
[tex]a = 14.4[/tex]units
[tex]b = 8.7[/tex]units
