SOLUTION: The base of a triangle exceeds the height by 4 inches. The area of the triangle is 30 square inches. Find the height of the triangle.

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Question 437046: The base of a triangle exceeds the height by 4 inches. The area of the triangle is 30 square inches. Find the height of the triangle.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The base of a triangle exceeds the height by 4 inches.
b+=+h%2B4
.
The area of the triangle is 30 square inches.
%281%2F2%29b%2Ah+=+30
.
Substitute for b = h+4
%281%2F2%29%2A%28h%2B4%29%2Ah+=+30
.
Multiply both sides by 2 to eliminate the 1/2.
%28h%2B4%29%2Ah+=+60
.
Multiply through the left side
h%5E2+%2B+4h+=+60
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Subtract 60 from both sides
h%5E2+%2B+4h+-+60+=+0
.
Factor the quadratic equation
%28h%2B10%29%28h-6%29+=+0
.
So h = -10 or h = 6
But a negative value for the height is nonsensical
So
h+=+6
.
Recall
b+=+h+%2B+4
That means that
b+=+10
.
Always check your work!
%281%2F2%29%2Ab%2Ah+=+%281%2F2%29%2810%29%286%29
%281%2F2%29%2810%29%286%29+=+30
That checks.
.
Review the question to be sure you answer it.
Answer: The height of the triangle is 6 inches.
.
Done.