The height of the triangle is 1 m greater than three times its base. The area of the triangle is 40m^2, what is the base of the triangle?

Answer:base = 5 mStep-by-step explanation:The area (A) of a triangle is calculated using the formulaA = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )here h = 3b + 1 ( 1 m greater than 3 times the base ), henceA = [tex]\frac{1}{2}[/tex] b(3b + 1) = 40Multiply both sides by 2b(3b + 1) = 80 ← distribute and rearrange3b² + b - 80 = 0 ← in standard formConsider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- termproduct = 3 × - 80 = - 240 and sum = 1The factors are - 15 and + 16Use these factors to split the b- term3b² - 15b + 16b - 80 = 0 ( factor the first/second and third/fourth terms )3b(b - 5) + 16(b - 5) = 0 ← factor out (b - 5)(b - 5)(3b + 16) = 0Equate each factor to zero and solve for bb - 5 = 0 ⇒ b = 53b + 16 = 0 ⇒ b = - [tex]\frac{16}{3}[/tex]However, b > 0 ⇒ b = 5The base of the triangle is 5 m