Question

What are the values of h and x in the right triangle?

Answer 1

h = 60, x = 25 (option B)

Step-by-step 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

`\begin{gathered} (144)/(156)=(156)/(x+144) \\ \text{cross multiply:} \\ 144(x\text{ + 144) = 1}56(156) \end{gathered}`
`\begin{gathered} 144x\text{ + 20736 = 24336} \\ 144x\text{ = 3600} \\ x\text{ = 3600/144} \\ x\text{ = 25} \end{gathered}`

To get height (h), apply geometric mean:

`\begin{gathered} (h)/(x)=(144)/(h) \\ h^2\text{ = 144(x)} \\ h^2=144(25) \\ h^2\text{ = 3600} \\ h\text{ = }\sqrt[]{3600} \\ h\text{ = 60} \end{gathered}`

h = 60, x = 25 (option B)