The sides

The sides of a rectangle are in the ratio 3:5, and its perimeter is 72 cm. Calculate:
a) the lengths of both sides of the rectangle,
b) the area of the rectangle,
c) the length of the diagonals.

Final 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

Row 2 - 2/5 · Row 1 → Row 2
5a-3b = 0
3.2b = 72


b = 72/3.2 = 22.5
a = 0+3b/5 = 0+3 · 22.5/5 = 13.5

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

Our linear equations calculator calculates it.

$b=22.5=22.5\text{cm}$

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

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

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