The height of a right triangle is 1 less than triple the base. the area of the triangle is 12 square inches. what is the base of the triangle?

Formula of Area of triangle A=1/2bh where A is area, b is the base, and h is height.

h= 3b-1

Area=12

At this point you want to plug in what you know into the equation.

12=1/2b(3b-1)

Then you can solve for b. First multiply each side by 2 to cancel the fraction.

24=b(3b-1)

Then distribute the b term.

24=3b^2 - b

Then set the equation equal to zero.

0=3b^2-b-24

Then either factor or use the quadratic equation to solve for b.

0=(3b-8)(b-3)

which means that b=3 and b=8/3

You then plug both answers back into the original equation (12=1/2b(3b-1))and see if there are any extraneous solutions. When you do, you can see that 8/3 as an answer does not equal 12. Therefore, the correct answer and the base of the triangle is equal to 3.

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step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt