Math problem algebra

Question

The base of a triangle is 6 inches more than 4 times the height. If the area of the triangle is 152 square inches, find the base and height.

Answer 1

I think it’s important to note that this problem gives 2 equations with 2 unknowns and is solved by solving one of the equations in terms of one of the unknowns and then substituting that in place of that unknown in the other equation as in line 4 of Raymond’s answer.

In Raymond’s Answer:

The first two lines are the two equations. The first line already has one of the unknowns in terms of the other.

The third line is the second line simplified getting the unknowns on one side alone but isn’t necessary.

The fourth line has the right side of the first equation substituted in place of b in the third line.

Then we solve for the other unknown h. Then we can substitute the value for h into either equation and solve for b.

Answer 2

b=6+4h

bh/2 = 152

bh=304

(6+4h)h = 304

4h^2+ 6h = 304

2h^2 +3h -152 = 0

factor or use the quadratic formula

(2h+19)(h-8) =0

h-8=0

h = 8 inch height

b= 6+4(8)=38 inch base

or if you couldn't see how to factor, use the quadratic formula

h =-3/4 + (1/4)sqr(9+8(152))= -3/4+ (1/4)sqr1225

=-3/4 +1/4(35) = 32/4= 8 inches=height

base = 6+4(8) =38 inches

area = bh/2 = 38(8)/2 = 304/2==152 in^2