Question

This is confusing me please helpppp

Answer 1

base = 12 cm

Altitude = 16 cm

Explanation:

Area of the triangle:

`\sf \boxed{Area \ of \ triangle = (1)/(2)*base*height}`

base = x cm

altitude or height = (x + 4) cm

`\sf (1)/(2)*x*(x+4) = 96\\\\`

x * (x + 4) = 96*2

x*x + x*4 = 192

x² + 4x = 192

x² + 4x - 192 = 0

Sum = 4

Product = -192

Factors = (-12) , 16

When we add (-12) & 16, we get 4. When we multiply (-12) & 16, we get (-192).

Rewrite the middle term using the factors.

x² + 16x - 12x - 192 = 0

x(x + 16) -12(x + 16) = 0

(x + 16)(x - 12) = 0

x - 12 = 0 or x + 16 = 0

x = 12 or x = -16

Ignore x = -16 as measurements won't be in negative value.

x = 12

Base = 12 cm

Altitude = 12 + 4 = 16 cm

Answer 2

base = 12 cm , altitude = 16 cm

Explanation:

the area (A) of a triangle is calculated as

A =
`(1)/(2)` ba ( b is the base and a the altitude )

here a = b + 4 , then

`(1)/(2)` b(b + 4) = 96 ( multiply both sides by 2 to clear the fraction )

b(b + 4) = 192

b² + 4b = 192 ( subtract 192 from both sides )

b² + 4b - 192 = 0 ← in standard quadratic form

(b + 16)(b - 12) = 0 ← in factored form

equate each factor to zero and solve for b

b + 16 = 0 ⇒ b = - 16

b - 12 = 0 ⇒ b = 12

however, b > 0 then b = 12

so base = 12 cm and altitude = b + 4 = 12 + 4 = 16 cm