Math  /  Geometry

QuestionWhat is the perimeter? If necessary, round to the nearest tenth. \square centimeters

Studdy Solution

STEP 1

1. We are given a right triangle.
2. Two sides are given: one side is 68 68 cm, and the other side is 51 51 cm.
3. We need to find the perimeter of the triangle, which is the sum of all its sides.
4. The hypotenuse is labeled as c c .

STEP 2

1. Use the Pythagorean Theorem to find the hypotenuse c c .
2. Calculate the perimeter by adding all three sides.

STEP 3

Use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (c c ) is equal to the sum of the squares of the other two sides. The formula is:
c2=a2+b2 c^2 = a^2 + b^2
where a=68 a = 68 cm and b=51 b = 51 cm.

STEP 4

Substitute the known values into the Pythagorean Theorem:
c2=682+512 c^2 = 68^2 + 51^2
Calculate the squares:
c2=4624+2601 c^2 = 4624 + 2601

STEP 5

Add the squares:
c2=7225 c^2 = 7225
Take the square root of both sides to solve for c c :
c=7225 c = \sqrt{7225}

STEP 6

Calculate the square root:
c=85 c = 85

STEP 7

Calculate the perimeter of the triangle by adding all three sides:
Perimeter=a+b+c \text{Perimeter} = a + b + c =68+51+85 = 68 + 51 + 85

STEP 8

Add the values:
Perimeter=204 \text{Perimeter} = 204
The perimeter of the triangle is:
204 cm \boxed{204} \text{ cm}

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