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6. The height of a triangle is 2 units more than the base. The area of the triangle is 10 square units. Find
the base to the nearest hundredth.


Sagot :

Answer:

4.24

Step-by-step explanation:

First, let's set up the equation: [tex]\frac{2+x^2}{2}=10[/tex]

Next, clear the fraction by multiplying both sides by 2:[tex]2*(\frac{2+x^2}{2}=10)=2+x^2=20[/tex]

Then, subtract 2 from both sides: [tex]x^2=18[/tex]

Finally, take a square root of both sides and round: [tex]\sqrt{x^2=18} =[/tex](Rounded to the nearest hundredth) 4.24

We will see that the base of the triangle measures 4 units.

How to find the base of the triangle?

For a triangle of base b and height h, the area is:

A = b*h/2

In this case, we know that:

A = 10 square units.

h = b + 2

Then we can write:

10 = b*h/2

If we replace the second equation into the above one, we get:

10 = b*(b + 2)/2

Now we can solve this for b:

[tex]20 = b^2 + b[/tex]

Then we need to solve the quadratic equation:

[tex]b^2 + b - 20 = 0[/tex]

The solutions are given by Bhaskara's formula.

[tex]b = \frac{-1 \pm \sqrt{1^2 - 4*1*(-20)} }{2} \\\\b = \frac{-1 \pm 9 }{2}[/tex]

The solution that we care for is the positive one:

b = (-1 + 9)/2 = 4

The base measures 4 units.

If you want to learn more about triangles:

https://brainly.com/question/2217700

#SPJ2

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