Answer: y = 6 mi. . ______________________________________________ Explanation: ______________________________________________ Area of a triangle = (½) * (base) * (height) ;
or, A = (½) * b * h ; or, A = b*h / 2 ; _____________________________________ Given: A = 24.3 mi ² ; b = 8.1 mi ___________________ Find the height, "h" ; (in units of "miles", or , "mi" ). __________________________ Plug in the known values into the formula:
24.3 mi ² = (½) * (8.1 mi) *(h) ; _____________________________ Solve for "h" (height) ; _____________________________ (½) * (8.1 mi) = 4.05 mi ; ______________________________ Rewrite: ____________________________ 24.3 mi² = (4.05 mi) *(h) ; Solve for "h" ; _________________________________________ Divide each side of the equation by "(4.05 mi)" ; to isolate "h" on one side of the equation ; and to solve for "h" ; __________________________________________ 24.3 mi² / 4.05 mi = (4.05 mi) *(h) / 4.05 mi ;
→ 6 mi = h ; ↔ h = 6 mi.
→ h = y = 6 mi. ____________________________________________
I'd suggest you begin with the formula for the area of a triangle of base b and height h. It is as follows:
bh A = -------- 2
Here b is the length of the base and h is the height of the triangle. In this problem the area and the base are given; they are 24.3 square miles and 8.1 miles respectively. We are to determine the height, y.
2A Solve the above equation for h, the height: 2A=bh, or ------- b
Substitute (24.3 square miles) for A and 8.1 miles for b.
Calculate y (or, equivalently, calculate h). Both represent the height of the given triangle.
