Answer:height = 15 yd
Base = 20 yd
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