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Alexxx [7]
2 years ago
13

The question is the photo.

Mathematics
2 answers:
andrew-mc [135]2 years ago
7 0

Answer:

w=5

Step-by-step explanation:

the triangle has the same size of area as the side of the rectangle so therefore 5

Liono4ka [1.6K]2 years ago
7 0

Answer:

The area of a triangle is A\Delta=\frac{1}{2}(base)(height)

So, the area of the given triangle is:

A\Delta=\frac{1}{2}(5)(6)\\A\Delta=\frac{1}{2}(30)\\A\Delta=15cm^2

The area of a rectangle is

A=(length)(width)\\A=(6)w\\A=6wcm^2

Once the area of both are the same:

6w=15\\w=\frac{15}{6} \\w=2.5cm

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1) Change radical forms to fractional exponents using the rule:
The n<span>th root of "</span>a number" = "that number" raised to the<span> reciprocal of n.
For example </span>\sqrt[n]{3} =   3^{ \frac{1}{n} }.

The square root of 3 (\sqrt{3}) = 3 to the one-half power (3^{ \frac{1}{2} }).
The 5th root of 3 (\sqrt[5]{3}) = 3 to the one-fifth power (3^{ \frac{1}{5} }).

2) Now use the product of powers exponent rule to simplify:
This rule says a^{m} a^{n} = a^{m+n}&#10;. When two expressions with the same base (a, in this example) are multiplied, you can add their exponents while keeping the same base.

You now have (3^{ \frac{1}{2} })*(3^{ \frac{1}{5} }). These two expressions have the same base, 3. That means you can add their exponents:
(3^{ \frac{1}{2} })(3^{ \frac{1}{5} })\\&#10;= 3^{(\frac{1}{2} + \frac{1}{5}) }\\&#10;= 3^{\frac{7}{10}}

3) You can leave it in the form 3^{\frac{7}{10}} or change it back into a radical \sqrt[10]{3^7}

------

Answer: 3^{\frac{7}{10}} or \sqrt[10]{3^7}
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