Answer:
Height = 3 inches and Base length = 7 inches
Step-by-step explanation:
1. Information provided to answer the question correctly:
Base of the triangle = x+ 4
Height of the triangle = x
Area of the triangle = 10.5 inches²
2. Find the base length and height
Let's recall the formula of the area of a triangle:
Area = (Base * Height)/2
Replacing with the values we know:
10.5 = x (x + 4)/2
21 = x² + 4x
x² + 4x - 21 = 0
(x + 7) (x - 3) = 0
(x₁ + 7) = 0 ⇒ x₁ = -7
(x₂ - 3) = 0 ⇒ x₂ = 3
We take x₂ as the answer because x₁ = -7 is not a valid height.
Height = 3 inches and Base length = 7 inches
