Question

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 1

Answer:

base = 5 m

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A = $\frac{1}{2}$ bh ( b is the base and h the height )

here h = 3b + 1 ( 1 m greater than 3 times the base ), hence

A = $\frac{1}{2}$ b(3b + 1) = 40

Multiply both sides by 2

b(3b + 1) = 80 ← distribute and rearrange

3b² + b - 80 = 0 ← in standard form

Consider 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- term

product = 3 × - 80 = - 240 and sum = 1

The factors are - 15 and + 16

Use these factors to split the b- term

3b² - 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) = 0

Equate each factor to zero and solve for b

b - 5 = 0 ⇒ b = 5

3b + 16 = 0 ⇒ b = - $\frac{16}{3}$

However, b > 0 ⇒ b = 5

The base of the triangle is 5 m