Question

Help asap!! Full work shown gets brainliest!!

Answer 1

Answer:

$b=2\sqrt{6}$

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 : $a^2+b^2=c^2$

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:

$a^2+b^2=c^2$

a = 5 and c = 7

$(5)^2+b^2=(7)^2$

simplify exponents 5² = 25 and 7² = 49

$25+b^2=49$

subtract 25 from both sides

$b^2=24$

take the square root of both sides

$b=\sqrt{24}$

simplify radical

$b=2\sqrt{6}$

And we are done!

Answer 2

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).

• $5^2 + b^2 = 7^2$
• $25 + b^2 = 49$
• $b^2=24$
• $b = \sqrt{24}$

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.
• $\sqrt{24} = \sqrt{4} * \sqrt{6} = 2\sqrt{6}$

Therefore, the answer is 2√6.