The height of a triangle is represented as (4x-2) inches, and the base of the triangle is twice its height. If the area of the triangle is 36 square inches, what is the value of x?

Answer 1

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"the height of the triangle is (4x-2), and the base of the triangle is twice its height"

height = 4x - 2

base = 2(4x-2).... distribute the two to get (8x-4) as the height

Area = 36 square inches

The formula for area of a triangle is A = (1/2)bh. Plug in the values that we know.

A = (1/2) bh

36 = (1/2) (8x - 4) (4x-2) (multiply 1/2 and the first expression)

36 = (4x - 2) (4x - 2) (Use FOIL to multiply the two expressions)

36 = 16x² - 16x + 4 (subtract 36 from each side to get 0 on the left side of the equation)

0 = 16x² - 16x - 32 (factor out a GCF of 16)

0 = 16 (x² - x - 2) (factor the polynomial)

0 = 16 (x - 2) (x + 1)

x - 2 = 0 means x could be 2

x + 1 = 0 means x could be -1

If you plug 2 into the original expressions for base and height you get:

height = 4x - 2 = 4(2) - 2 = 6

base = 8x - 4 = 8(2) - 4 = 12

A = (1/2)(12)(6) = 36

IT WORKS!! x = 2

If you plug -1 into the original expressions for base and height you get:

height = 4x - 2 = 4(-1) - 2 = -10 (it is impossible to have a negative length for height of a triangle)

base = 8x - 4 = 8(-1)) - 4 = -20 (impossible to have a negative lengths for base of a triangle)

x can not equal -1

Final Answer: x = 2

Answer 2

Answer: x=2, -1

We know the formula for the area of a triangle is A=1/2bh

A=36

b=2(4x-2) The height, multiplied by 2

h=4x-2

36=1/2(2(4x-2))(4x-2) Plug in each value into A=1/2bh

36=1/2(8x-4)(4x-2) First distribute inside the left parentheses

36=(4x-2)(4x-2) You can distribute the 1/2 first, or foil first, you should end up with the same answe

36=16x²-8x-8x+4 Foil then combine like terms

36=16x²-16x+4 Subtract 36 to the other side

16x²-16x-32=0 Factor out a 16

16(x²-x-2)=0 Factor the inside; two numbers that add to -1 and multiply to -2

(x-2)(x+1) Take the opposite of the insides of the parentheses for your answer

x=2, -1

If you plug in both values of x into the original equation, they both equal to 36 sq inches, therefore x could be either value.