SmokeyRN
07.07.2019 •
Mathematics
The base of a triangle exceeds the height by 7 feet. if the area is 114 square feet, find the length of the base and the height of the triangle.
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Ответ:
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. ?
Ответ:
"-9.1d" and "6f+9.1"
Step-by-step explanation: