Question

100 points gor correct answer Identify the base of a triangle in which h=(3x+15) ft and A=(15x+75) ft^2.

Answer 1

Answer:

b = 10

Step-by-step explanation:

The area (A) of a triangle is calculated as

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

Here h = 3x + 15 and A = 15x + 75, thus

$\frac{1}{2}$ × b × (3x + 15) = 15x + 75

Multiply both sides by 2 to clear the fraction

b(3x + 15) = 30x + 150

Divide both sides by (3x + 15)

b = $\frac{30x+150}{3x+15}$ ← factor numerator and denominator

  = $\frac{30(x + 5)}{3(x+5)}$ ← cancel the factor (x + 5) on numerator/denominator

  = $\frac{30}{3}$

  = 10

Answer 2

Answer:

b = 10ft

Step-by-step explanation:

Area = ½ × base × height

15x + 75 = ½ × base × (3x + 15)

30x + 150 = base × (3x + 15)

10(3x + 15) = base × (3x + 15)

base = 10