Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 12a^5 and 9a^5.

Answers

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Step-by-step explanation:

Step-by-step explanation:

Since the length of both legs of the right angle triangle are given, we would determine the hypotenuse, h by applying Pythagoras theorem which is expressed as

Hypotenuse² = one leg² + other leg²

Therefore,

h² = (3a)³ + (4a)³

h² = 27a³ + 64a³

h² = 91a³

Taking square root of both sides,

h = √91a³

The formula for determining the perimeter of a triangle is expressed as

Perimeter = a + b + c

a, b and c are the side length of the triangle. Therefore, the expression for the perimeter of the right angle triangle is

√91a³ + (3a)³ + (4a)³

= √91a³ + 91a³

Step-by-step explanation:

a^{2} + b ^{2}  = c^{2}

[ (3a)^{3} ]^{2} + [ (4a)^{3} ]^{2} = C^{2}  

I'm assuming the length was (3a)^{3}, not 3a^{3}.

It was difficult to tell in your question.

(3a)^{6} +(4a)^{6} = C^{2}

729a^{6} + 4096a^{6} = C^{2}  

4825a^{6} = c^{2}    

Take the square root of both sides.

69.4622a^{3} ≈ c

hope someone helps you for know im trying to figure it out

Step-by-step explanation:

36a^5.

Step-by-step explanation:

In a right angle triangle,

Length of one leg =12a^5

Length of other leg =9a^5

According to the Pythagoras theorem,

Hypotenuse^2=leg_1^2+leg_2^2

Using Pythagoras theorem,

Hypotenuse^2=(12a^5)^2+(9a^5)^2

Hypotenuse^2=144(a^5)^2+81(a^5)^2

Hypotenuse=\sqrt{225(a^5)^2}

Hypotenuse=15a^5

Perimeter of right angle triangle is the sum of all sides of the triangle.

Perimeter=12a^5+9a^5+15a^5

Perimeter=36a^5  units.

Therefore, the required expression is 36a^5.

106.4622 a^{3}

Step-by-step explanation:

Given the information:

A right triangleLeg lengths of (3a)^{3} and (4a)^{3}

Use the pytagon theory to find the hypotenuse of the triangle

a^{2}  + b^{2}  = c^{2}

<=>((3a)^{3}) ^{2}  + ((4a)^{3}) ^{2}  = c^{2}

<=>(3a)^{6} + (4a)^{6} = c^{2}  

<=> c^{2}  = 4285a^{6}

Take the square root of both sides

<=> c = 69.4622 a^{3}

=> expression in simplest form for the perimeter of a right triangle is:

(3a)^{3} + (4a)^{3} + 69.4622 a^{3}  

= 27a^{3}  + 64a^{3}  + 69.4622 a^{3}  

= 106.4622 a^{3}

48a^4

Step-by-step explanation:

 In this case we know that the  legs of the given right triangle have these lenghts:

12a^4 and 16a^4

By definition, the sides of a right triangle are in the ratio 3:4:5

Since:

\frac{5}{4}=1.25

We can multiply the lenght  16a^4 by 1.25 in order to find the lenght of the hypotenuse of the right triangle:

(16a^4)(1.25)=20a^4

Since the perimeter of a triangle is the sum of the lenghts of its sides, we can write the following expression for the perimeter of the given right triangle:

12a^4+16a^4+20a^4

Simplifying, we get:

=48a^4



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