585/2 for exact form
292.5 for decimal form
292 1/2 for mixed number form
The Law of Cosines is useful for this.
d² = e² + f² - 2ef·cos(D)
cos(D) = (e² + f² - d²)/(2ef) = (1.8² + 3.1² - 2²)/(2·1.8·3.1)
D = arccos(8.85/11.16)
D ≈ 37.5°
Answer:
Perimeter of ABCD - Perimeter of PQRS = 4x + 2
Step-by-step explanation:
i. For rectangle ABCD;
length, l = 2x -3
width, w = 4x + 5
Perimeter of a rectangle = 2(l + w)
Perimeter of ABCD = 2((2x -3) + (4x + 5))
= 2(2x -3 + 4x + 5)
= 2(6x + 2)
Perimeter of ABCD = 12x + 4
ii. For rectangle PQRS;
length, l = x - 1
width, w = 3x + 2
Perimeter of a rectangle = 2(l + w)
Perimeter of PQRS = 2((x - 1) + (3x + 2))
= 2(x - 1 + 3x + 2)
= 2(4x + 1)
Perimeter of PQRS = 8x + 2
So that,
Perimeter of ABCD - Perimeter of PQRS = (12x + 4) - (8x + 2)
= 12x + 4 - 8x - 2
= 4x + 2
Perimeter of ABCD - Perimeter of PQRS = 4x + 2