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The area of a triangle is 12 square meters . The base is 2 meters longer than the height Find the height of the triangle .

Sagot :

xKelvin

Answer:

The height of the triangle is four meters.

Step-by-step explanation:

We are given that the area of a triangle is 12 square meters. The base is two meters longer than the height, and we want to determine the height of the triangle.

Recall that the area of a triangle is given by:

[tex]\displaystyle A = \frac{1}{2}bh[/tex]

Since the area is 12 square meters:

[tex]\displaystyle 12 = \frac{1}{2}bh[/tex]

The base is two meters longer than the height. In other words, we can write that:

[tex]b = h + 2[/tex]

Substitute:

[tex]\displaystyle 12=\frac{1}{2}(h+2)h[/tex]

Solve for h. Multiply both sides by two:

[tex]24 = (h+2)h[/tex]

Distribute:

[tex]h^2+2h=24[/tex]

Isolate:

[tex]h^2+2h-24=0[/tex]

Factor:

[tex](h+6)(h-4)=0[/tex]

Zero Product Property:

[tex]h + 6 = 0\text{ or } h -4 =0[/tex]

Solve for each case:

[tex]h = -6\text{ or } h = 4[/tex]

Since the height cannot be negative, we can ignore the first solution.

Thus, the height of the triangle is four meters.

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