Math  /  Geometry

Question-3 Quiz The ratio of the measures of the sides of a triangle is 9:7:39: 7: 3. If the perimeter of the triangle is 266 inches, find the length of the shortest side.

Studdy Solution

STEP 1

1. The sides of the triangle are in the ratio 9:7:39:7:3.
2. The perimeter of the triangle is 266266 inches.
3. We need to find the length of the shortest side.

STEP 2

1. Express the side lengths in terms of a common variable.
2. Set up an equation for the perimeter.
3. Solve for the common variable.
4. Calculate the length of the shortest side.

STEP 3

Let the common variable be xx. Then the sides of the triangle can be expressed as: - First side: 9x9x - Second side: 7x7x - Third side: 3x3x

STEP 4

The perimeter of the triangle is the sum of its sides. Set up the equation for the perimeter: 9x+7x+3x=266 9x + 7x + 3x = 266

STEP 5

Combine the terms and solve for xx: 19x=266 19x = 266 x=26619 x = \frac{266}{19}

STEP 6

Calculate the length of the shortest side, which is 3x3x: 3x=3×26619 3x = 3 \times \frac{266}{19} 3x=79819 3x = \frac{798}{19} 3x=42 3x = 42
The length of the shortest side is:
42 \boxed{42}

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