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Step2247 [10]
3 years ago
12

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

Mathematics
1 answer:
WITCHER [35]3 years ago
6 0

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

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