Answer:
10 inches
Step-by-step explanation:
The area of a triangle is expressed as [tex]1/2bh[/tex] where;
g b is the lenghth of the base
h is the height
If the height of the triangle is 4 less than it’s base, then h = b-4
Substituting h = b-4 into the formula we have;
[tex]A = \frac{1}{2}*b*(b-4)[/tex]
Given Area of the triangle A = 30in²
30 = [tex]\frac{{b^{2}-4b} }{2}[/tex]
Cross multiplying;
60 = b²-4b
b²-4b-60 = 0
b²-10b+6b-60 = 0
b(b-10)+6(b-10)=0
(b+6)(b-10) = 0
b+6 = 0 and b- 10 = 0
b = -6 and 10
Choosing the positive base;
b = 10 in
The length of the base to the nearest inch is 10 inches
