Isabellacattidn
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Sagot :

Renkneeidn

Answer:

2√6

Step-by-step explanation:

1. First, let's solve for the base of the triangle with the help of the Pythagorean Theorem (a^2 + b^2 = c^2).

  • [tex]5^2 + b^2 = 7^2[/tex]
  • [tex]25 + b^2 = 49[/tex]
  • [tex]b^2=24[/tex]
  • [tex]b = \sqrt{24}[/tex]

2. Now, let's find the factors of 24 and see which one is a perfect square:

  • 1, 2, 3, 4, 6, 8, 12, 24
  • As you can see, the factor that's a perfect square is 4, so in order for it to multiply to 24, the other one has to be 6.
  • [tex]\sqrt{24} = \sqrt{4} * \sqrt{6} = 2\sqrt{6}[/tex]

Therefore, the answer is 2√6.

SenorMathWizidn

Answer:

[tex]b=2\sqrt{6}[/tex]

Step-by-step explanation:

The triangle shown is a right triangle.

Because this triangle is a right triangle, we can use they Pythagorean theorem to find the missing side length.

Pythagorean theorem : [tex]a^2+b^2=c^2[/tex]

where a and b = length of legs and c = hypotenuse ( longest side )

we have the hypotenuse ( 7 ) and a leg (5) and need to find the other leg.

So we know that a = 5 and c = 7 and we need to find b

Using the Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex]

a = 5 and c = 7

[tex](5)^2+b^2=(7)^2[/tex]

simplify exponents 5² = 25 and 7² = 49

[tex]25+b^2=49[/tex]

subtract 25 from both sides

[tex]b^2=24[/tex]

take the square root of both sides

[tex]b=\sqrt{24}[/tex]

simplify radical

[tex]b=2\sqrt{6}[/tex]

And we are done!

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