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.
The ratio of the surface areas of similar solids is equal to the square of their scale factor and that the ratio of their volumes is equal to the cube of their scale factor.
