Question

The altitude of a triangle is 1cm shorter than the base. If the area of the triangle is 15cm2, calculate the altitude.

Answer 1

Answer:

5 cm

Step-by-step explanation:

We khow that the altitude of this triangle is 1cm shorter than the base

• Let H be our altitude and B our base and A the area of the triangle
• A= (B*H)/2 ⇒ 15=(B*H)/2
• H is 1cm shorter than B ⇒ B=H+1
• H*(H+1)/2=15 ⇒ H*(H+1)=30⇒ H²+H=30⇒H²+H-30+0

that's a quadratic equation . Let's calculate the dicriminant .

Let Δ be the dicriminant

• a=1
• b=1
• c= -30
• Δ=b²-4*a*c = 1²-4*1*(-30)=1+4*30=121≥0
• Δ≥0⇔ that we have two solutions x and y
• x= (-1-$\sqrt{121}$)/2= (-1-11)/2= -6
• y= (-1+$\sqrt{121}$)/2= 10/2 = 5

We have a negative value and a positive one

The altitude is a distance so it can't be negative

H= 5cm