Respuesta :
Answer:
The height of Triangle is 12 yd and
The base of Triangle is 31 yd
Step-by-step explanation:
Given as :
The area of triangle = 186 yd²
Let the height of triangle = h
So, base of triangle = 7 + 2 h
Now,
∵ The area of triangle = [tex]\frac{1}{2}\times base\times height[/tex]
Or, 186 yd² = [tex]\frac{1}{2}\times (7+2h)\times h[/tex]
Or, 186 × 2 = h × ( 7 +2h )
Or, 372 = 7 h + 2 h²
Or, 2 h² + 7 h - 372 = 0
So , 2 h² - 24 h + 31 h - 372 = 0
Or, 2 h ( h - 12 ) + 31 ( h - 12 ) = 0
Or, ( h - 12 ) ( 2 h + 31 ) = 0
SO, h - 12 = 0 And 2 h + 31 = 0
∴ h = 12 yd And h = [tex]\frac{-31}{2}[/tex]
SO, the Height of triangle = h = 12 yd and
The base of triangle = 2 × 12 + 7 = 24 + 7 = 31 yd
Base = 31 yd
Hence The height of Triangle is 12 yd and The base of Triangle is 31 yd Answer
