Trapezoid arm

Calculate the arm length b of the trapezoid ABCD if a = 12 cm, c = 4 cm, the length of AC is same as the length of BC and the area S of the triangle ABC is 9 cm square.

Final Answer:

b =  6.1847 cm

Step-by-step explanation:

$$\begin{gathered} a=12\text{cm} \\ c=4\text{cm} \\ S=9{\text{cm}}^2 \\ S=\frac{a\cdot v}{2} \\ v=2\cdot S/a=2\cdot 9/12=\frac{3}{2}=1.5\text{cm} \\ {b}^2=v^2+(a/2{)}^2 \\ b=\sqrt{v^2+(a/2{)}^2}=\sqrt{1.5^2+(12/2{)}^2}=6.1847\text{cm} \end{gathered}$$

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