Question

5)

What is the perimeter of the triangle?
(2x + 4) in.
5 in.
MALA
(3x - 2) in.

Answer 1

Perimeter = 10x + 6

Area = √(
`5x^2` + 11x + 4)

Angle measures can be found using the law of cosines.

Perimeter:

AB = 5 (given)

AC = 3x - 2 (given)

BC = 2x + 4 (given)

Perimeter = AB + AC + BC = 5 + (3x - 2) + (2x + 4) = 10x + 6

Area:

We can use Heron's formula to find the area of a triangle when we know all the side lengths. Heron's formula states:

Area = √(s(s - a)(s - b)(s - c))

where s is the semiperimeter (half of the perimeter), a, b, and c are the side lengths of the triangle.

In this case, the semiperimeter s = (10x + 6)/2 = 5x + 3.

Substituting the side lengths and semiperimeter into Heron's formula:

Area = √((5x + 3)((5x + 3) - 5)((5x + 3) - (3x - 2))((5x + 3) - (2x + 4)))

This simplifies to:

Area = √(
`5x^2` + 11x + 4)

Angle Measures:

We can use the law of cosines to find the measures of all angles in a triangle when we know all the side lengths. The law of cosines states:

cos(C) = (
`a^2 + b^2 - c^2`) / 2ab

where C is the angle opposite to side c, and a and b are the other two sides.

In this case, we can use the sides BC, AB, and AC to find angle C:

cos(C) = (
`(2x + 4)^2 + 5^2 - (3x - 2)^2`) / (2(2x + 4)(5))

This simplifies to:

cos(C) = (
`9x^2`- 28x + 49) / (50x + 40)

Once you have the value of cos(C), you can use the inverse cosine function (cos^-1) to find angle C. Similarly, you can find the other angles using the law of cosines with different side combinations.

Perimeter = 10x + 6

Area = √(
`5x^2` + 11x + 4)

Angle measures can be found using the law of cosines.

The question probable may be:

What is the perimeter of the triangle? 5 in. (2x + 4) in. (3x - 2) in.