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kondor19780726 [428]
3 years ago
5

Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 3a cubed and 4a cubed

Mathematics
1 answer:
Over [174]3 years ago
8 0

Answer:

106.4622 a^{3}

Step-by-step explanation:

Given the information:

  • A right triangle
  • Leg 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}

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If ab = 8 and a^2+b^2=16, then what is the value of (a+b)^2?
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ab = 8 & a^{2} + b^{2} = 16 so , ( a+b )^{2} = 32 .

<u>Step-by-step explanation:</u>

Here we have , ab= 8 & a^2+b^2=16 i.e. ab = 8  and a^{2} + b^{2} = 16 .

We need to find value of (a+b)^2 i.e. (a+b)^{2} :

It's and identity and we know that ( a+b )^{2} = a^{2} +b^{2} +2ab

⇒ ( a+b )^{2} = a^{2} +b^{2} +2ab

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2 years ago
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