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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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Answer:

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Step-by-step explanation:

If two given points on any line equation  are A(a,b) and B(c,d).

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Noe, here the points are given as (c,4) and (2,6)

So, the slope m = \frac{6-4}{2-c}    =\frac{2}{2-c}\\\implies  m =\frac{2}{2-c}

Hence, the slope of the given points is  m = \frac{2}{2-c}

3 0
3 years ago
A model airplane is built to a scale of 1 in.:12 ft. If the model plane is 11 inches long, find the length of the actual plane,
torisob [31]

Answer:

132 feet

Step-by-step explanation:

we know that

The scale is equal to \frac{1}{12}\ \frac{in}{ft}

That means ---> 1 inch in the model represent 12 feet in the actual

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4 0
3 years ago
Solve this equation.
cestrela7 [59]

Answer:

OB=4

Step-by-step explanation:

Step 1: Subtract 5 from both sides.

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Step 2: Divide both sides by 4.

4x/4=16/4

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Answer:

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8 0
3 years ago
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hram777 [196]

Answer:

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Step-by-step explanation:

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1. What is the area of the trapezoid? The diagram is not drawn to scale. (1 point)
Dmitry [639]

Answer:

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Step-by-step explanation:

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\frac{1}{2} (7+17) * 5

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= 12*5

= 60

8 0
3 years ago
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