Question

MATH 100 POINTS
THANK you

Answer 1

The value of x of the given triangle is: 1.49 meters

What is the area of the triangle?

The formula for the area of a triangle with two sides and an angle is:

Area of triangle = ½ × A * C * cos B

We are given:

A = (x + 5)

C = (3x - 2)

Area = 4√2

Thus:

4√2 = ½ × (x + 5) × (3x - 2) × cos 45

4√2 = ½ × (x + 5) × (3x - 2) × 1/√2

Multiply both sides by 2√2 to get:

16 = 3x² + 17x - 10

3x² + 17x - 16 = 0

Using quadratic equation calculator gives:

x = 1.49 meters

Answer 2

x = 1.49

Step-by-step explanation:

area of triangle given angle between adjacent sides:

`Area \ of \ triangle = (1)/(2) AB \ cos(C)`

Applying this formula:

`\sf 4√(2) = (1)/(2)(x+5)(3x-2) \ cos(45)`

`\sf 4√(2) = (1)/(2)(x+5)(3x-2) * (√(2))/(2)`

`\sf 4√(2) = (√(2))/(4)(x+5)(3x-2)`

`\sf 16 =(x+5)(3x-2)`

`\sf 16 =3x^2 -2x +15x-10`

`\sf 3x^2 -2x +15x-10-16=0`

`\sf 3x^2 +13x-26=0`

`\sf x = (-13\pm√(481) )/(6)`

`\sf x =1.49, \ -5.82`

As value of Length can be only positive and cannot be negative so:

`\sf x =1.49 \ \ (only)`