The altitude of a triangle is 1cm shorter than the base. If the area of the triangle is 15cm2, calculate the altitude.
1 answer:
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-
)/2= (-1-11)/2= -6
- y= (-1+
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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Answer:
(-∞, -2), (-2, -0.618), and (1.618, 3)
Step-by-step explanation:
The red plus (+) signs indicate the regions in which the function is concave up, and the red negative (-) signs indicate the regions in which the function is concave down.
Note that the sign of the concavity changes at an inflection point.
Let's examine the intervals given.
(-∞, -2): Yes, concave up.
(-∞, -1.17): No. Concave up in (-∞, -2) but concave down in (-2, -1.17).
(-2, 0): No. Concave down in (-2, -1.17) but increasing in (-1.17, 0.0).
(-1.17, 0.689): Yes. Concave up.
(-0.618, 1.618): No. Concave up in (-0.618, 0.689) but concave down in (0.689, 1.618).
(0, 3): No. Concave up in (0, 0.689), concave down in (0.689, 2.481), and concave up in (2.481, 3).
(2.481, ∞): Yes. Concave up.
The three intervals that are concave up are (-∞, -2), (-1.17, -0.689), and (2.481, ∞).
