Math / Geometry

QuestionWhat is the value of $x$ in simplest radical form?

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. The legs of the triangle are 12 and 35.
3. The hypotenuse is labeled as $x$ .
4. We will use the Pythagorean Theorem to solve for $x$ .

STEP 2

1. Recall the Pythagorean Theorem.
2. Substitute the known values into the theorem.
3. Solve for $x^2$ .
4. Simplify to find $x$ in simplest radical form.

STEP 3

Recall the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse $c$ is equal to the sum of the squares of the lengths of the other two sides $a$ and $b$ :
$c^2 = a^2 + b^2$

STEP 4

Substitute the known values into the Pythagorean Theorem. Here, $a = 12$ , $b = 35$ , and $c = x$ :
$x^2 = 12^2 + 35^2$

STEP 5

Calculate the squares of the legs:
$x^2 = 144 + 1225$

STEP 6

Add the results:
$x^2 = 1369$

STEP 7

Take the square root of both sides to solve for $x$ :
$x = \sqrt{1369}$

STEP 8

Recognize that 1369 is a perfect square:
$x = 37$
The value of $x$ in simplest radical form is:
$\boxed{37}$

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QuestionWhat is the value of $x$ in simplest radical form?

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. The legs of the triangle are 12 and 35.
3. The hypotenuse is labeled as $x$ .
4. We will use the Pythagorean Theorem to solve for $x$ .

STEP 2

1. Recall the Pythagorean Theorem.
2. Substitute the known values into the theorem.
3. Solve for $x^2$ .
4. Simplify to find $x$ in simplest radical form.

STEP 3

Recall the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse $c$ is equal to the sum of the squares of the lengths of the other two sides $a$ and $b$ :
$c^2 = a^2 + b^2$

STEP 4

Substitute the known values into the Pythagorean Theorem. Here, $a = 12$ , $b = 35$ , and $c = x$ :
$x^2 = 12^2 + 35^2$

STEP 5

Calculate the squares of the legs:
$x^2 = 144 + 1225$

STEP 6

Add the results:
$x^2 = 1369$

STEP 7

Take the square root of both sides to solve for $x$ :
$x = \sqrt{1369}$

STEP 8

Recognize that 1369 is a perfect square:
$x = 37$
The value of $x$ in simplest radical form is:
$\boxed{37}$

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QuestionWhat is the value of xxx in simplest radical form?

Studdy Solution

STEP 1

1. The triangle is a right triangle.2. The legs of the triangle are 12 and 35.3. The hypotenuse is labeled as x x x.4. We will use the Pythagorean Theorem to solve for x x x.

STEP 2

1. Recall the Pythagorean Theorem.2. Substitute the known values into the theorem.3. Solve for x2 x^2 x2.4. Simplify to find x x x in simplest radical form.

STEP 3

Recall the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse c c c is equal to the sum of the squares of the lengths of the other two sides a a a and b b b:c2=a2+b2 c^2 = a^2 + b^2 c2=a2+b2

STEP 4

Substitute the known values into the Pythagorean Theorem. Here, a=12 a = 12 a=12, b=35 b = 35 b=35, and c=x c = x c=x:x2=122+352 x^2 = 12^2 + 35^2 x2=122+352

STEP 5

Calculate the squares of the legs:x2=144+1225 x^2 = 144 + 1225 x2=144+1225

STEP 6

Add the results:x2=1369 x^2 = 1369 x2=1369

STEP 7

Take the square root of both sides to solve for x x x:x=1369 x = \sqrt{1369} x=1369​

STEP 8

Recognize that 1369 is a perfect square:x=37 x = 37 x=37 The value of x x x in simplest radical form is:37 \boxed{37} 37​

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QuestionWhat is the value of $x$ in simplest radical form?

1. The triangle is a right triangle.
2. The legs of the triangle are 12 and 35.
3. The hypotenuse is labeled as $x$ .
4. We will use the Pythagorean Theorem to solve for $x$ .

1. Recall the Pythagorean Theorem.
2. Substitute the known values into the theorem.
3. Solve for $x^2$ .
4. Simplify to find $x$ in simplest radical form.

Recall the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse $c$ is equal to the sum of the squares of the lengths of the other two sides $a$ and $b$ :
$c^2 = a^2 + b^2$

Substitute the known values into the Pythagorean Theorem. Here, $a = 12$ , $b = 35$ , and $c = x$ :
$x^2 = 12^2 + 35^2$

Calculate the squares of the legs:
$x^2 = 144 + 1225$

Add the results:
$x^2 = 1369$

Take the square root of both sides to solve for $x$ :
$x = \sqrt{1369}$

Recognize that 1369 is a perfect square:
$x = 37$
The value of $x$ in simplest radical form is:
$\boxed{37}$