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Find the height if the triangle if the area is 10.26 cm

Find the height if the triangle if the area is 10.26 cm-example-1
User Alec Wenzowski
by
3.0k points

1 Answer

21 votes
21 votes

So, here we have that area is 10.26cm2.

We know that the equation to find area of a triangle is (bh)/2.

If we replace, we have:

A= (bh)/2, -----> 10.26=(bh)/2 -------> 20.52=bh (equation 1)

If we want to find "h", the best thing we can do here is to use Pythagoras theorem. Then, we got this equation:

8^2 - (2.7+x)^2= h^2

64 - (7.29 + 5.4x + x^2) = h^2

56.71 - 5.4x - x^2 = h^2 (equation 2)

where x is the rest of the side.

Now, we have two equations, right?

So we are going to find h in function of x.

If 20.52 = bh, then h=(b/20.52). But we know that b is equal to (2.7+x)

So the equation will be:

h=(2.7+x)/(20.52) (Equation 3).

If we equal equations 3 and 1:

h^2 = 56.71 - 5.4x - x^2 = h^2

And, h^2 = (7.29 + 5.4x + x^2)/421.0704 ( Applied (2.7+x)^2)

We have that h^2 = h^2, so

56.71 - 5.4x - x^2 =

Then we have a quadratic equation, and if we solve it, we obtain x=

User Nuageux
by
3.0k points
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