Question

The perimeter of a triangle is 16x−6. If two sides measure 3x+2 and 4x−9, then how long is the third side?

Answer 1

To find the length of the third side of the triangle, use the formula for the perimeter of a triangle and solve for the third side.

Step-by-step explanation:

To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle.

The formula is P = a + b + c, where P is the perimeter and a, b, and c are the lengths of the sides.

In this case, the perimeter is given as 16x - 6, and the lengths of the first two sides are 3x + 2 and 4x - 9.

So, the equation becomes 16x - 6 = (3x + 2) + (4x - 9) + c.

Simplifying the equation, we get 16x - 6 = 7x - 7 + c.

Now, we can solve for c by subtracting 7x and 7 from both sides of the equation.

This gives us 9x - 13 = c.

Therefore, the length of the third side is 9x - 13.

Answer 2

Perimeter of a triangle is the sum of measures of its all three sides, let the other be y,

we know,

`\hookrightarrow \: y + 3x + 2 + 4x - 9 = 16x - 6`

`\hookrightarrow \: y + 7x - 7 = 16x - 6`

`\hookrightarrow \: y = 16x - 6 - 7x + 7`

`\hookrightarrow \: y = 6x + 1`

hence, measure of the third side is 6x + 1