# The right triangle

The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.

Correct result:

b =  30 cm
t2 =  39 cm

#### Solution:

$a=36 \ \text{cm} \ \\ S=540 \ \text{cm}^2 \ \\ \ \\ S=\dfrac{ ab }{ 2 } \ \\ \ \\ b=2 \cdot \ S/a=2 \cdot \ 540/36=30 \ \text{cm}$
$t_{2}^2=a^2 + (b/2)^2 \ \\ t_{2}=\sqrt{ a^2 + (b/2)^2 }=\sqrt{ 36^2 + (30/2)^2 }=39 \ \text{cm}$

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