SOLUTION: the height of a tower is 68 ft more than three times a side of its square base. if the sum of these two dimesions is 1380 feet, find the height of the tower. Help!!!! any clue??

Question 73743: the height of a tower is 68 ft more than three times a side of its square base. if the sum of these two dimesions is 1380 feet, find the height of the tower.
Help!!!! any clue????
Thanks in advance
Found 2 solutions by jim_thompson5910, bucky:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let h=height, s=side of square base
Using the word problem as the clue to what h equals we see that

If the sum of the height and the side is 1380 it translates to this:

Plug in 68+3s into h
Solve for s

So the side's length is 656 ft, use this to find the height

So the height of the tower is 1,052 ft tall
Check:

works
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Call the side of its square base S. Then 3 times the side of its square base is 3S. The
height (call it H) of the tower is said to be 68 feet more than 3S. So in equation form
the height H can be expressed as our first equation:
.
H = 3S + 68
.
The problem then says the sum of H and S is 1380 feet. In equation form this second
equation is:
.
H + S = 1380
.
We now have two independent equations, both involving H and S. These are the conditions
you need to solve a pair of linear equations. One of the ways to solve such equations
is by substitution. We can use that method here. Note that the first equation gives an
expression for H in terms of S. We can take the right side of that equation and substitute it
for H in the second equation. When we do the second equation becomes:
.
(3S + 68) + S = 1380
.
On the left side combine the two terms that contain S to get:
.
4S + 68 = 1380
.
Next eliminate the 68 on the left side by subtracting 68 from both sides to get:
.
4S = 1312
.
Solve for S by dividing both sides by 4 to get:
.
S = 1312/4 = 328 feet
.
So now we know that the base is a square that is 328 feet on a side.
.
Knowing this we can now return to either of the first two equations and substitute
328 feet for S so that we can solve for H.
.
For example, let's return to the second equation that says:
.
H + S = 1380
.
Substitute 328 for S and get:
.
H + 328 = 1380
.
Get rid of the 328 feet on the left side by subtracting 328 from both sides to get:
.
H = 1380 - 328 = 1052 feet
.
That completes the problem.
.
Hope that this helps you work your way through it and gives you some insight into the
general process of solving sets of linear equations.
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