Right trapezoid

The right trapezoid has bases 3.2 cm and 62 mm long. The shorter leg has a length of 0.25 dm. Calculate the lengths of the diagonals and the second leg.

Correct answer:

u₁ =  6.6851 cm
u₂ =  4.0608 cm
b =  3.9051 cm

Step-by-step explanation:

$$\begin{gathered} a=62\text{ mm}\to \text{ cm}=62\mathrm{/}10\text{ cm}=6.2\text{ cm } \\ c=3.2\text{ cm } \\ d=0.25\text{ dm}\to \text{ cm}=0.25\cdot 10\text{ cm}=2.5\text{ cm } \\ {u}_1^2=d^2+a^2 \\ {u}_1=\sqrt{d^2+a^2}=\sqrt{2.5^2+6.2^2}=6.6851\text{ cm} \end{gathered}$$

$$\begin{gathered} u_2^2=d^2+c^2 \\ {u}_2=\sqrt{d^2+c^2}=\sqrt{2.5^2+3.2^2}=4.0608\text{ cm} \end{gathered}$$

$$\begin{gathered} b^2=d^2+(a-c{)}^2 \\ b=\sqrt{d^2+(a-c{)}^2}=\sqrt{2.5^2+(6.2-3.2{)}^2}=3.9051\text{ cm} \end{gathered}$$

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