h = 60, x = 25 (option B)
Explanation:
x/leg 1 =leg 1/ (x + 144)
leg 1 = 65
144/leg 2 = leg 2/(x + 144)
leg 2 = 156
To avoid a quadratic equation, we will go with the equation having leg 2
[tex]\begin{gathered} \frac{144}{156}=\frac{156}{x+144} \\ \text{cross multiply:} \\ 144(x\text{ + 144) = 1}56(156) \end{gathered}[/tex][tex]\begin{gathered} 144x\text{ + 20736 = 24336} \\ 144x\text{ = 3600} \\ x\text{ = 3600/144} \\ x\text{ = 25} \end{gathered}[/tex]
To get height (h), apply geometric mean:
[tex]\begin{gathered} \frac{h}{x}=\frac{144}{h} \\ h^2\text{ = 144(x)} \\ h^2=144(25) \\ h^2\text{ = 3600} \\ h\text{ = }\sqrt[]{3600} \\ h\text{ = 60} \end{gathered}[/tex]
h = 60, x = 25 (option B)
