Answer:
b = 10
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here h = 3x + 15 and A = 15x + 75, thus
[tex]\frac{1}{2}[/tex] × 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 = [tex]\frac{30x+150}{3x+15}[/tex] ← factor numerator and denominator
= [tex]\frac{30(x + 5)}{3(x+5)}[/tex] ← cancel the factor (x + 5) on numerator/denominator
= [tex]\frac{30}{3}[/tex]
= 10
