Answer:
5 cm
Step-by-step explanation:
Area= 1/2 base×altitude
let base be x cm hence altitude = x+7 cm
30 = 1/2 (x) (x+7)
60= x^2 + 7x
x = 5 or - 12
but measurements can't be in negative form hence -12 is discarded. Thus x= 5 cm
x= base hence base = 5cm
Answer:
base = 5 cm
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 altitude )
let base be b then h = b + 7
Given A = 30, then
[tex]\frac{1}{2}[/tex]b(b + 7) = 30 ( multiply both sides by 2 to clear the fraction )
b(b + 7) = 60 ← distribute left side
b² + 7 = 60 ( subtract 60 from both sides )
b² + 7 - 60 = 0 ← in standard form
(b + 12)(b - 5) = 0 ← in factored form
Equate each factor to zero and solve for b
b + 12 = 0 ⇒ b = - 12
b - 5 = 0 ⇒ b = 5
However, b > 0, thus b = 5
That is the base is 5 cm
