Let h represent the height. Then the base is h+6 (all measurements are in feet).
The formula for the area of a triangle is A = (base)(height)/2.
Here A = 114 ft^2 = (base)(height)/2. Substituting the (h+6) and h,
A = [114 ft^2] = [(h+6)(h)]/2 , or [h^2 + 6h]/2, or 2A = 228 = (h+6)h. Multiply out the right side
Solve 228 = h^2 + 6h for h:
h^2 + 6h - 228 = 0
Applying the Quadratic Formula, -6 plus or minus sqrt(36-4(1)(-228)) h = ------------------------------------------------- 2 -6 plus or minus sqrt(948) -6 plus or minus 30.79 or h = ------------------------------------- = ------------------------------------ 2 2 -6 plus or minus 30.79 h = ---------------------------------- 2
We want only the positive result. That comes to h = 30.79-6 ---------- 2
or 24.79/2, or h = 12. 40
h represents the altitude of the triangle, so h+7 represents the length of the base. These values are 12.40 feet and 19.40 feet respectively.
Substitute b=19.40 feet and h=12.40 feet into the formula A = bh/2. Is the result 114 sq. ft. ?
Your current CD matures in a few days. You would like to find an investment with a higher rate of return than the CD. Stocks historically have a rate of return between 10% and 12%, but you do not like the risk involved. You have been looking at bond listings in the newspaper. A friend wants you to look at the following corporate bonds as a possible investment.
