Question

The roof of a shack has a slope of 1/4

Answer 1

`x\text{ = 28}`

Here, we want to find the value of x in the diagram, given the value of the slope

From the question, we have two points, separated by a horizontal distance

Mathematiclly the slope of a line is;

`\begin{gathered} m\text{ = }(\Delta y)/(\Delta x) \\ \\ m\text{ = }(12-0)/(\Delta x) \\ \\ (1)/(4)\text{ = }(12)/(\Delta x) \\ \\ \Delta x\text{ = 4}*12 \\ \\ =\text{ 48} \end{gathered}`

Now, what this mean is that, the x value from the tip of the triangle to the dotted line represented by 12 is 48

This is not the value of x, we want to calculate

Now, the x-distance from the tip of the rectangle to the dotted line marked as 5 is (48-x)

Thus, we have it that;

`\begin{gathered} (1)/(4)\text{ = }(5)/(48-x) \\ \\ 4(5)\text{ = 48-x} \\ \\ 20\text{ = 48-x} \\ \\ x\text{ = 48-20} \\ \\ x\text{ = 28} \end{gathered}`