What are the dimensions of the triangle if the area is 150 yd.² the height is X + 5 base is 3X - 10

Answer:height = 15 yd

Base = 20 yd

Step-by-step explanation:

The formula for determining the area of a rectangle is expressed as

Area = 1/2 base * height.

From the information given, the area of the triangle is 150 yd.² the height is x + 5 and the base is 3x - 10.

Therefore,

150 = 1/2 * (3x - 10) (x + 5)

300 = 3x^2 + 15x - 10x - 50

300 + 50 = 3x^2 + 5x

350 = 3x^2 + 5x

3x^2 + 5x - 350 = 0

3x^2 + 35x - 30x - 350 = 0

x (3x + 35) - 10 (3x + 35) = 0

x - 10 = 0 or 3x + 35 = 0

x = 10 or x = - 35/3

Since the dimensions cannot be negative, then x = 10

The height = x + 5 = 10 + 5 = 15 yd

The base = 3x - 10 = 3*10 - 10 = 20 yd