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How do you find the length of the hypotenuse of a triangle with sides of length √5m and 3√2m?

1 Answer

Jun 10, 2016

$\sqrt{23}$ $sqrt(23)$

Explanation:

A right-angled triangle with legs of lengths $a$ $a$ and $b$ $b$ , and a hypotenuse of $c$ $c$ has the lengths of its sides specified by the Pythagorean Theorem:
$XXX c^{2} = a^{2} + b^{2}$ $color(white)("XXX")c^2=a^2+b^2$

For the given case $a = \sqrt{5} m$ $a=sqrt(5) m$ and $b = 3 \sqrt{2} m$ $b=3sqrt(2) m$

Therefore
$XXX c^{2} = {(\sqrt{5})}^{2} + {(3 \sqrt{2})}^{2}$ $color(white)("XXX")c^2=(sqrt(5))^2+(3sqrt(2))^2$

$XXXX = 5 + 18$ $color(white)("XXXX")=5+18$

$XXXX = 23$ $color(white)("XXXX")=23$

So
$XXX c = \sqrt{23}$ $color(white)("XXX")c=sqrt(23)$

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