# Right trapezoid

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

Correct result:

u1 =  6.685 cm
u2 =  4.061 cm
b =  3.905 cm

#### Solution:

$a=62 \ mm \rightarrow cm=62 / 10 \ cm=6.2 \ cm \ \\ c=3.2 \ \text{cm} \ \\ d=0.25 \ dm \rightarrow cm=0.25 \cdot \ 10 \ cm=2.5 \ cm \ \\ \ \\ u_{1}^2=d^2 + a^2 \ \\ u_{1}=\sqrt{ d^2 + a^2 }=\sqrt{ 2.5^2 + 6.2^2 }=6.685 \ \text{cm}$
$u_{2}^2=d^2 + c^2 \ \\ u_{2}=\sqrt{ d^2 + c^2 }=\sqrt{ 2.5^2 + 3.2^2 }=4.061 \ \text{cm}$
$b^2=d^2 + (a-c)^2 \ \\ b=\sqrt{ d^2 + (a-c)^2 }=\sqrt{ 2.5^2 + (6.2-3.2)^2 }=3.905 \ \text{cm}$

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