The height of a triangle is 6x and the base is (3x + 10) cm. The area of the triangle is 816 sq. cm. What are the dimensions of the base and the height of the triangle?

Height: 48

Base: 34

Step-by-step explanation:

The formula for a triangle is 1/2(base)(height)

1/2(3x+10)(6x) = 816

18x² + 60x = 1632

18x² + 60x - 1632 = 0

Then, we use the Quadratic formula

x = (-60 ± √3600 + 117,504)/36

x =( -60 ± 348/36)

x = 288/36

x = 8

3(8) + 10

= 34

6(8) = 48

Therefore the dimensions are:

Height: 48

Base: 34

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.