A triangle with an area of 140 square inches has a height that is two less than three times the base

Question

Find the base and the height of the triangle

Answer 1

A=bh/2

We know that the height is two less than 3 times the base, making the equation of,

H=3b-2

Sub "h" into the area equation,

140= (b(3b-2))/2

Factor out the "b" into (3b-2),

140= 3b^2-2b/2

To, get rid of "/2" multiply each side by 2 to cancel it out,

140(2)= 3b^2-2b

280=3b^2-2b

Move everything to one side to factor the equation,

=3b^2-2b-280

To factor, we have to know the factors of 280 to ensure that we are using the correct numbers to factor,

1x280=280

2x 140=280

4x70=280

5x56=280

7x40=280

8x35=280

10x28=280

14x20=280

Factor out the equation 3b^2-2b-280

(b-10)(3b+28)

To know you chose the correct one plug into the factor and solve

3bxb+28b-30b-280= 3b^2-2b-280

Set each factor equal to zero and solve,

b-10=0

b=10

3b+28=0

3b=-28

b=-9.33

Notice that one one answer is negative, when we are looking for the measurement we don't use negative numbers so we cancel that one out, and are left with the correct answer

b=10

Plug b into the height "h" equation and solve,

H=3(10)-2

H=30-2

H=28

Those are your height and base answers (:

Answer 2

Some hints:

What is it asking me to do?

What do I know, what am I given?

What is the formula for the area of a triangle?

b = base, ht = height

140square inches = 1/b x ht

How do we translate the words "has a height that is two less than three times the base"

into an algebraic equation.

"is" means "="

"two less than" means "subtract to from..."

"3 times the base" means " 3 multiplied by the base(b)

Thus in words you get :

ht. = 3b - 2

NEXT STEP

USE SUBSTITUTION TO SOLVE for "B" and "h" and find the height and base of the triable.

Last: check your answer by putting it back into one of the two equations: 140 = 1/2b x ht or ht = 3b -2

Hope this helps, hopefully you know where to take it from there.