Answer:
Question 15: x = 17
Question 16: area = 5610 units
Step-by-step explanation:
Question 15:
The perimeter is the sum of all sides of a triangle.
It is given that the perimeter is 374 units.
[tex]p = 8x - 4 + 9x + 4 + 4x + 17[/tex]
[tex]374 = 8x - 4 + 9x + 4 + 4x + 17[/tex]
Add all the like terms.
[tex]374 = 21x + 17[/tex]
Subtract 17 from both sides.
[tex]357 = 21x[/tex]
Divide by 21 from both sides.
[tex]17 = x[/tex]
Question 16:
The area of a triangle can be found by using the following formula:
[tex]a = \frac{1}{2} bh[/tex]
(where a is the area, b is the base, and h is the height)
Using the value of x you just found previously (17), you can calculate the base and height by substituting 17 with x in their respective equations.
[tex]h = 8x - 4[/tex]
[tex]h = 8(17) - 4[/tex]
[tex]h = 134[/tex]
[tex]b = 4x + 17[/tex]
[tex]b = 4(17) + 17[/tex]
[tex]b = 85[/tex]
Now that you found the base and height, substitute the values, 134 and 75, into the area of a triangle formula.
[tex]a = \frac{1}{2} bh[/tex]
[tex]a = \frac{1}{2} (85)(132)[/tex]
[tex]a = 5610[/tex]
