De stelling van Pythagoras met bewijs

$3^{2} - 4 \cdot \frac{1}{2} \cdot 2 \cdot 1 = 5$ . Klopt.

$5^{2} - 4 \cdot \frac{1}{2} \cdot 2 \cdot 3 = 13$

$A$ : 4; 4; 8
$B$ : 2; 4; 10
$C$ : 2; 8; 10
$D$ : 5; 10; 17

$A$ en $C$

Oefenen met de stelling van Pythagoras

$a = 3$ ; $b = 12$ ; $c = 3$ ; $d = 6$ ; $e = 6$ ; $f = 5$ ; $g = 3$

Berekening $a$ :
$6^{2} + 8^{2} = a^{2}$
$36 + 64 = a^{2}$ $100 = a^{2}$
$a = 10$

Berekening $b$ :
$12^{2} + 35^{2} = b^{2}$
$144 + 1225 = b^{2}$ $1369 = b^{2}$
$b = 37$

Berekening $c$ :
$80^{2} + 18^{2} = c^{2}$
$6400 + 324 = c^{2}$ $6724 = c^{2}$
$c = 82$

Berekening $x$ :
$16^{2} + x^{2} = 34^{2}$
$x^{2} = 900$
$x = 30$

Berekening $y$ :
$y^{2} + 60^{2} = 61^{2}$
$y^{2} = 121$
$y = 11$

Berekening $m$ :
$24^{2} + 7^{2} = m^{2}$
$m^{2} = 625$
$m = 25$

Berekening $n$ :
$16^{2} + 63^{2} = n^{2}$
$n^{2} = 4225$
$n = 65$

Berekening $p$ :
$p^{2} + 20^{2} = 101^{2}$
$p^{2} = 9801$
$p = 99$

$x^{2} = 84^{2} + 13^{2} = 7225$
$x = 85$ dm

$y^{2} + 36^{2} = 85^{2}$
$y^{2} = 5929$
$y = 77$ dm

Volgens de stelling van Pythagoras geldt:
$x^{2} + 45^{2} = {(75 - x)}^{2}$
$x^{2} + 2025 = 5625 - 150 x + x^{2}$
$150 x = 3600$
$x = 24$

$x^{2} = 5^{2} + 12^{2} = 169$
Dus $x = 13$ .
De foto is 13 bij 18 cm.

$x^{2} + 10^{2} = 26^{2}$
$x^{2} = 576$
$x = 24$
$hoogte = 24 + 2 = 26$ m