Question

A triangle has a base of x^1/3 m and a height of x^1/2 m. If the area of the triangle is 16 m^2​, what are the base and height of the​ triangle?

The base is....and the height is......

Answer 1

Area = (base times height) / 2

Can rewrite it as

A= b * h * 1/2

16 = (x^(1/3)) * ( x^(1/2)) * (1/2))
Multiply by 2 to simplify
32 = x^(1/3) * x^(1/2)
32=x ^(5/6)
X=64

Base = 4
Height = 8

Please look below at how you multiply variables that have fractions as exponents (you need to add the exponents, common denominator and all that)

Answer 2

The base of the triangle is 4 m and the height of the triangle is 8 m.

What is the area of the triangle?

The are of the triangle is A = 1/2 × b × h

where 'b' is the base and 'h' is the height

For given example,

A triangle has a base of x^1/3 m and a height of x^1/2 m.

Also, the area of the triangle is 16 m^2​

⇒ $b = x^{\frac{1}{3}} ~m,h=x^{\frac{1}{2} }~m, A=16~m^{2}$

Using the formula for area of the triangle,

$\Rightarrow A=\frac{1}{2}\times b\times h\\\\\Rightarrow 16=\frac{1}{2}\times x^{\frac{1}{3} }\times x^{\frac{1}{2} }\\\\\Rightarrow 16\times 2=x^{\frac{1}{3} + \frac{1}{2} }\\\\\Rightarrow 32=x^{\frac{5}{6} }\\\\\Rightarrow 32^6=(x^{\frac{5}{6} })^6\\\\\Rightarrow 32^6=x^5\\\\\Rightarrow x=32^{\frac{6}{5}}\\\\\Rightarrow x=64$

So, the base of the triangle would be,

$\Rightarrow b=x^{\frac{1}{3} }\\\\\Rightarrow b=64^{\frac{1}{3} }\\\\\Rightarrow \bold{b=4}$

and the height of the triangle would be,

$\Rightarrow h=x^{\frac{1}{2}}\\\\\Rightarrow h=64^{\frac{1}{2} }\\\\\Rightarrow \bold{h=8}$

Therefore, the base of the triangle is 4 m and the height of the triangle is 8 m.

Learn more about the area of the triangle here:

https://brainly.com/question/27683633

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