SOLUTION: The area of a triangle is 34 cm^2. If the base of the triangle is increased by 5 cm, the area of the triangle would be 51cm^2. How long is the base of the triangle?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The area of a triangle is 34 cm^2. If the base of the triangle is increased by 5 cm, the area of the triangle would be 51cm^2. How long is the base of the triangle?       Log On


   

Question 919552: The area of a triangle is 34 cm^2. If the base of the triangle is increased by 5 cm, the area of the triangle would be 51cm^2. How long is the base of the triangle?
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a triangle is 34 cm^2. If the base of the triangle is increased by 5 cm, the area of the triangle would be 51cm^2. How long is the base of the triangle?
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Area = (1/2)(base)(height)
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Original Area:: 34 = (1/2)(b*h)
b*h = 68
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New Area::
51 = (1/2)(b+5)h
102 = bh + 5h
102 = 68 + 5h
5h = 34
h = 6.8
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Ans: b = bh/h = 68/6.8 = 10 cm
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Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The area of a triangle is:A=%281%2F2%29b%2Ah
given
A=34+cm%5E2=> %281%2F2%29b%2Ah=34cm%5E2..........eq.1

If the base of the triangle is increased by 5cm, the area of the triangle would be 51cm%5E2.

%281%2F2%29%28b%2B5cm%29%2Ah=51cm%5E2..........eq.2
How long is the base of the triangle?
solve the system:
%281%2F2%29b%2Ah=34cm%5E2..........eq.1
%281%2F2%29%28b%2B5cm%29%2Ah=51cm%5E2..........eq.2
_________________________________________subtract 1 from 2
%281%2F2%29%28b%2B5cm%29%2Ah-%281%2F2%29b%2Ah=51cm%5E2-34cm%5E2
%281%2F2%29%28%28b%2B5cm%29%2Ah-b%2Ah%29=17cm%5E2
cross%28b%2Ah%29%2B5cm%2Ah-cross%28b%2Ah%29=2%2A17cm%5E2
5cm%2Ah=34cm%5E2
h=34cm%5E2%2F5cm
h=6.8cm
go to eq.1 and plug in 6.8cm for h
%281%2F2%29b%2A6.8cm=34cm%5E2..........eq.1.....solve for b
%281%2Fcross%282%29%29b%2Across%286.8%293.4cm=34cm%5E2
b%2A3.4cm=34cm%5E2
b=34cm%5E2%2F3.4cm
b=340cm%5E2%2F34cm
highlight%28b=10cm%29 ...the base of the triangle