Shape area order

Arrange the given shapes according to their area, in descending order:
S - Square with perimeter = 16 cm
O - A rectangle with side a = 3 cm and perimeter o = 16 cm
T - A right-angled triangle with a hypotenuse of 4.125 cm and a hypotenuse of 8.125 cm

Final Answer:

x = TOS

Step-by-step explanation:

$$\begin{gathered} o_1=16\text{cm} \\ {a}_1=o_1/4=16/4=4\text{cm} \\ {S}_1=a_1^2=4^2=16{\text{cm}}^2 \\ {a}_2=3\text{cm} \\ {o}_2=16\text{cm} \\ {b}_2=o_2/2-a_2=16/2-3=5\text{cm} \\ {S}_2=a_2\cdot b_2=3\cdot 5=15{\text{cm}}^2 \\ {a}_3=4.125\text{cm} \\ {c}_3=8.125\text{cm} \\ {b}_3=\sqrt{c_3^2-a_3^2}=\sqrt{8.125^2-4.125^2}=7\text{cm} \\ {S}_3=\frac{a_3\cdot b_3}{2}=\frac{4.125\cdot 7}{2}=\frac{231}{16}=14\frac{7}{16}=14.4375{\text{cm}}^2 \\ {S}_3<S_2<S_1 \\ x=TOS \end{gathered}$$

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