Answer:
16.81 and 12.25
Step-by-step explanation:
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. ?
4*5 is 20
add 2 zeroes to the end because of the two you took out from 40 and 50
40*50=2000
If he traveled x mi by bus, then the time taken using bus is x/40 hours
and therefore, she took (580-x) mi by train, thus the time taken with train was (580-x)/80 hours.
Hence, x/40 +(580-x)/80 = 9.5 hours
80(x/40) +80 (580-x)/80 = (9.5)80
= 2x + 580-x = 760
x= 760-580
x = 180
Thus the train covered a distance of (580-x) =580-180 = 400
Hence, Wendy took 400/80 = 5 hours on the train
