Isosceles Trapezoid Arm Length

Diagonal alpha equals 0.4 m, and diagonal beta equals 0.4 m in the isosceles trapezoid. Side AB is 120 cm, and side DC is 7.6 dm. Find the length of arms in an isosceles trapezoid. Please result round to 2 decimal places.

Final Answer:

r =  102.3719 cm

Step-by-step explanation:

$$\begin{gathered} u=1.4\text{m}\to \text{cm}=1.4\cdot 100\text{cm}=140\text{cm} \\ a=120\text{cm} \\ c=7.6\text{dm}\to \text{cm}=7.6\cdot 10\text{cm}=76\text{cm} \\ x=(a-c)/2=(120-76)/2=22\text{cm} \\ h=\sqrt{u^2-(c+x{)}^2}=\sqrt{140^2-(76+22{)}^2}=14\sqrt{51}\text{cm}\doteq 99.98\text{cm} \\ r=\sqrt{h^2+x^2}=\sqrt{99.98^2+22^2}=4\sqrt{655}=102.3719\text{cm} \end{gathered}$$

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