Answer:
The base of triangle is
and the height of triangle is ![\frac{12}{\sqrt{3}} \ m.](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B%5Csqrt%7B3%7D%7D%20%5C%20m.)
Step-by-step explanation:
Given:
A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of the triangle is 16m to the power of 2.
Now, to find the base and height of the triangle.
The base of triangle = ![x\times\frac{1}{2} =\frac{x}{2} \ m.](https://tex.z-dn.net/?f=x%5Ctimes%5Cfrac%7B1%7D%7B2%7D%20%3D%5Cfrac%7Bx%7D%7B2%7D%20%5C%20m.)
The height of triangle = ![x\times \frac{3}{4} =\frac{3x}{4}\ m.](https://tex.z-dn.net/?f=x%5Ctimes%20%5Cfrac%7B3%7D%7B4%7D%20%3D%5Cfrac%7B3x%7D%7B4%7D%5C%20m.)
The area of triangle = ![16\ m^2.](https://tex.z-dn.net/?f=16%5C%20m%5E2.)
Now, we put the formula of area to solve:
![Area=\frac{1}{2} \times base\times height](https://tex.z-dn.net/?f=Area%3D%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20base%5Ctimes%20height)
![16=\frac{1}{2} \times \frac{x}{2} \times \frac{3x}{4}](https://tex.z-dn.net/?f=16%3D%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7Bx%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7B3x%7D%7B4%7D)
![16=\frac{3x^2}{16}](https://tex.z-dn.net/?f=16%3D%5Cfrac%7B3x%5E2%7D%7B16%7D)
<em>Multiplying both sides by 16 we get:</em>
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<em>Dividing both sides by 3 we get:</em>
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<em>Using square root on both sides we get:</em>
![\frac{16}{\sqrt{3}}=x](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B%5Csqrt%7B3%7D%7D%3Dx)
![x=\frac{16}{\sqrt{3}}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B16%7D%7B%5Csqrt%7B3%7D%7D)
Now, by substituting the value of
to get the base and height:
![Base=\frac{x}{2}\\\\Base=\frac{\frac{16}{\sqrt{3}}}{2} \\\\Base=\frac{8}{\sqrt{3}} \ m.](https://tex.z-dn.net/?f=Base%3D%5Cfrac%7Bx%7D%7B2%7D%5C%5C%5C%5CBase%3D%5Cfrac%7B%5Cfrac%7B16%7D%7B%5Csqrt%7B3%7D%7D%7D%7B2%7D%20%5C%5C%5C%5CBase%3D%5Cfrac%7B8%7D%7B%5Csqrt%7B3%7D%7D%20%5C%20m.)
<em>So, the base of triangle = </em>
<em />
![Height=x\times\frac{3}{4} \\\\Height=\frac{16}{\sqrt{3}}\times \frac{3}{4} \\\\Height=\frac{12}{\sqrt{3}} \ m.](https://tex.z-dn.net/?f=Height%3Dx%5Ctimes%5Cfrac%7B3%7D%7B4%7D%20%5C%5C%5C%5CHeight%3D%5Cfrac%7B16%7D%7B%5Csqrt%7B3%7D%7D%5Ctimes%20%5Cfrac%7B3%7D%7B4%7D%20%5C%5C%5C%5CHeight%3D%5Cfrac%7B12%7D%7B%5Csqrt%7B3%7D%7D%20%5C%20m.)
<em>Thus, the height of triangle = </em>
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Therefore, the base of triangle is
and the height of triangle is ![\frac{12}{\sqrt{3}} \ m.](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B%5Csqrt%7B3%7D%7D%20%5C%20m.)