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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