A triangle has base 2x+1 and height 6x-3. What value of x would give an area of 240 m2? Round to the nearest hundredth.

Answer 1

The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height.

In this case, we are given that the area is 240 m2 and the base is 2x+1. We need to solve for x.

240 = (1/2)(2x+1)(6x-3)

Multiplying both sides by 2 to eliminate the denominator:

480 = (2x+1)(6x-3)

Distributing on the right side:

480 = 12x^2 - 6x + 6x - 3

Combining like terms:

480 = 12x^2 - 3

Rearranging to isolate the quadratic term:

12x^2 = 480 +3

12x^2 = 483

Dividing both sides by 12:

x^2 = 483/12

x^2 = 40.25

To get x, we take the square root of both sides:

x = √(40.25)

x ≈ 6.34 (rounded to hundredth)

Therefore, the value of x that would give an area of 240 m2 is approximately 6.34.