Question

Using quadratic equations, find the height and base lengths of a triangle that has an area of 24 cm2 and height 2 cm more than its base.

Answer 1

Base=6cm

Height=8cm

Explanation:

A=1/2BH

24=1/2X(X+2)(X)

24=1/2(X2+2X)

48=X2+2X

X2+2X-48=0

axb=-48

a+b=2

X2+8X-6X-48=0

X(X+8)-6(X+8)=0

(X-6)(X+8)=0

X=6 or X=-8

Base= 6cm

Height=6+2=8cm

Answer 2

x = the length of the base

x+2 = the length of the height

we know that the area = 24cm²

the area of ​​a triangle = (base*h)/2

[x(x+2)]/2 = 24

(x²+2x)/2 = 24

(x²+2x)/2-24=0

x²+2x-48=0

b²-4ac =2²-4(1*-48)=196

Δ= 196

(-b-√Δ)= (-2-14)/2 =-8

(-b+√Δ)/2a =(-2+14)/2=6

a length is never negative,

x= 6

the base = 6cm

the height = 8cm

A=(6*8)/2=24cm²