If c is the measure of the hypotenuse of a right triangle, how do you find each missing measure given a=x, b=x+41, c=85?

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Answer 1 · 2017-03-07T16:17:52

36 & 77

We know, In a right triangle, $hypotenuse^2 = base^2+height^2$

Here, $c^2 = a^2 + b^2$

$rArr 85^2 = x^2 + (x+41)^2$

$rArr 7225 = x^2+x^2+82x+1681$

$rArr 2x^2+82x+1681-7225=0$

$rArr$ 2x^2 + 82x - 5544=0#

$rArr 2(x^2+41x-2772)=0$

$rArr x^2+41x-2772 = 0$

$rArr x^2+77x-36x-2772 = 0$

$rArr x(x+77)-36(x+77)=0$

$rArr (x-36)(x+77)=0$

$rArr x = 36 & -77$ $[x != -77]$

Hence a = 36 & b = 36+41 = 77