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

Height: 48 cm

Base: 34 cm

Step-by-step explanation:

Area = ½ * base * height

816 = ½ * (3x + 10) * (6x)

1632 = 18x² + 60x

3x² + 10x - 272 = 0

3x² + 34x - 24x - 272 = 0

x (3x + 34) - 8 (3x + 34) = 0

(3x + 34) (x - 8) = 0

x = - 34/3, 8

x = 8

Dimensions:

6x = 6 (8) = 48

3x + 10 = 3 (8) + 10 = 34

height = 48cm

Base = 34cm

Step-by-step explanation:

The area of a triangle is found by

A = 1/2 bh where b is the base and h is the height

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

= 1/2*3x (3x+10)

= 3x * (3x+10)

Distribute

= 9x^2 + 30x

The area of a triangle is 816

816 = 9x^2 + 30x

Subtract 816 from each side

816-816 = 9x^2 + 30x-816

0 = 9x^2 + 30x-816

Factor out a 3

0 = 3 (3x^2 + 10x - 272)

Factor

0=3 (3x + 34) (x-8)

Using the zero product property

3x+34 = 0 x-8 = 0

3x = - 34 x=8

x = - 34/3 x=8

Since we cannot have a negative length

x=8

height = 6x = 6*8 = 48

Base = 3x+10 = 3*8+10 = 34