The sides

The sides of the rectangle are in a ratio of 3: 5 and its circumference measures 72 cm. Calculate:
a) the size of both sides of the rectangle
b) the area of the rectangle
c) the length of the diagonals

Correct answer:

a =  13.5 cm
b =  22.5 cm
S =  303.75 cm²
u =  26.2393 cm

Step-by-step explanation:

5a=3b
2(a+b)=72

5•a=3•b
2•(a+b)=72

5a-3b = 0
2a+2b = 72

a = 27/2 = 13.5
b = 45/2 = 22.5

Our linear equations calculator calculates it.

$b=22.5={\displaystyle \frac{45}{2}}={\displaystyle \frac{45}{2}}\text{ cm}=22.5\text{ cm}$

$S=a\cdot b=13.5\cdot 22.5={\displaystyle \frac{1215}{4}}={\displaystyle \frac{1215}{4}}{\text{cm}}^2=303.75{\text{cm}}^2$

$u=\sqrt{a^2+b^2}=\sqrt{13.5^2+22.5^2}=26.2393\text{ cm}$

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