SOLUTION: Help me solve this problem please: The height of a triangle is 4 cm more than twice the length of the base. The area of the triangle is 35 cm(squared). Find the height of the tria

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Question 916909: Help me solve this problem please:
The height of a triangle is 4 cm more than twice the length of the base. The area of the triangle is 35 cm(squared). Find the height of the triangle.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The height of a triangle is k cm more than m times the length of the base. The area of the triangle is A cm(squared). Find the height of the triangle.

Area formula: %281%2F2%29bh=A
A, area
b, base
h, height
Description: h=k%2Bmb


STEPS FOR SOLUTION IN SYMBOLIC FORM
h-k=mb
b=%28h-k%29%2Fm
-
%281%2F2%29%28%28h-k%29%2Fm%29h=A

%28h-k%29h=A%2A2%2Am
h%5E2-kh-2mA=0
You can continue purely in symbolic form or you could substitute the given values now.

h%5E2-4h-2%2A2%2A35=0
h%5E2-4h-140=0
%28h%2B10%29%28h-14%29=0
Two solutions to the equation.
h=-10 makes no meaningful sense.
highlight%28h=14%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Help me solve this problem please:
The height of a triangle is 4 cm more than twice the length of the base. The area of the triangle is 35 cm(squared). Find the height of the triangle.


Let height be H

Then base-length = %28H+-+4%29%2F2

Since area = 35, then we can say that: %281%2F2%29%28H%29%28%28H+-+4%29%2F2%29+=+35

%28H%28H+-+4%29%29%2F4+=+35

H%5E2+-+4H+=+140} ----- Cross-multiplying

H%5E2+-+4H+-+140+=+0

(H - 14)(H + 10) = 0

H, or height = highlight_green%2814%29 cm               OR              H+=+-+10 (ignore)