Answer:
Height = 28 inches, Base = 36 inches
Step-by-step explanation:
Height of a triangle is 4x inches and the base is (5x+1) inches.
Area of the triangle is given as 500 square inches.
We have to calculate the dimensions of the triangle.
Since area of a triangle = (1/2)×Base×height = 500
(1/2)×(4x)×(5x+1) = 500
2x(5x+1) = 500
x(5x+1) = 250
5x² + x - 250 = 0
[tex]x=\frac{-1\pm \sqrt{1+20\times 250}}{2\times 5}[/tex]
[tex]=\frac{-1\pm \sqrt{5001}}{10}=\frac{-1\pm 70.72}{10}[/tex]
x = 7
Therefore height = 4x = 28 inches
Base = (5x + 1) = 35+1 = 36 inches.
