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Dafna11 [192]
3 years ago
7

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

Mathematics
1 answer:
tatiyna3 years ago
7 0

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 = 14.4units

So, the sides are:

a = 14.4units

b = 8.7units

Answer:

a = 14.4units

b = 8.7units


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