Question

Length of base of a triangle is 2 more than its height if area is 48 squares form a quadratic equation to find the base and height ​

Answer 1

Answer:

Base = (4√6+1) cm

Height = (4√6-1) cm

Step-by-step explanation:

Let the height be h

Therefore, base = (h+2)

Also, given that,

Area = 48 cm sq.

But, we know that,

Area of triangle = ½ × base × height

Substitute the respective values to get,

=> ½ × (h+2) × h = 48

=> h(h+2) = 48×2

=> h^2 + 2h = 96

=> h^2 + 2h - 96 = 0

=> h = {-2 ± √(2^2 -4(1)(-96))}/2(1)

=> h = (-2±√(4+382))/2

=> h = (-2±√386)/2

=> h = (-2±2√96)/2

=> h = -1±√96

=> h = -1±4√6

But length can't be negative.

Therefore,

=> Height = -1+4√6 cm

And

=> Base = 1+4√6 cm