Question 437046
The base of a triangle exceeds the height by 4 inches.
{{{b = h+4}}}
.
The area of the triangle is 30 square inches.
{{{(1/2)b*h = 30}}}
.
Substitute for b = h+4
{{{(1/2)*(h+4)*h = 30}}}
.
Multiply both sides by 2 to eliminate the 1/2.
{{{(h+4)*h = 60}}}
.
Multiply through the left side
{{{h^2 + 4h = 60}}}
.
Subtract 60 from both sides
{{{h^2 + 4h - 60 = 0}}}
.
Factor the quadratic equation
{{{(h+10)(h-6) = 0}}}
.
So h = -10 or h = 6
But a negative value for the height is nonsensical
So
{{{h = 6}}}
.
Recall
{{{b = h + 4}}}
That means that
{{{b = 10}}}
.
Always check your work!
{{{(1/2)*b*h = (1/2)(10)(6)}}}
{{{(1/2)(10)(6) = 30}}}
That checks.
.
Review the question to be sure you answer it.
Answer:  The height of the triangle is 6 inches.
.
Done.