Question 1167042
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<pre>

H = height

length = H+9


Diagonal 


    H^2 + (H+9)^2 = 45^2


    2H^2 + 18H + 81 = 2025

    2H^2 + 18H - 1944 = 0

     H^2 + 9H - 972 = 0


Factor


    (H-27)*(H+36) = 0


The roots are  H= 27  and  H= -36.


Only positive root works.


<U>ANSWER</U>.  The height is 27 inches.
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Solved.


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<U>A post-solution notice</U>


<pre>
    This triangle is nothing else as a famous (3,4,5)-right angled triangle with the similarity factor of 9.
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