Question

Find the sides of a rectangle having area 125 square units if the sides are in the ratio 5:3.

Answer 1

For this case we have the following data:

Area of the rectangle, $A = 125$

Relationship of the sides 5: 3

By definition, the area of a rectangle is given by:

$A = a * b$

Where

• a: is the longest side.

• b: it is the side of least length.

If the sides have a 5: 3 ratio, it means:

$\frac{a}{b}=\frac{5}{3}$

$a=\frac{5}{3}b$

Substituting in the formula of the area, we have:

$125 =a * b$

$125=\frac{5}{3}b*b$

Clearing b:

$3 * 125 = 5 * b ^ 2$

$\frac{375}{5}= b ^ 2$

$75 = b ^ 2$

$b =\sqrt{75}b = 8.7$ units

Substituting and clearing:

$125 = a * 8.7$

$a =\frac{125}{8.7}$

$a = 14.4$units

So, the sides are:

$a = 14.4$units

$b = 8.7$units

Answer:

$a = 14.4$units

$b = 8.7$units