Let L and W be the length and width of the given rectangle, respectively. Perimeter is calculated through the equation,
P = 2L + 2W
Substituting the perimeter,
36 = 2L + 2W
Simplifying,
18 = L + W
The area is calculated by multiplying the length and width as below,
A = 80 = LW
Substituting the expressions,
80 = (L)(18 - L)
The value of L from the equation is 8. With this, the value of W is equal to 10.
Therefore, the dimensions of the rectangle are 8 m by 10 m.
Answer: option d. the argument is valid by the law of detachment.
The law of detachment consists in make a conlcusion in this way:
Premise 1) a => b
Premise 2) a is true
Conclusion: Then, b is true
Note: the order of the premises 1 and 2 does not modifiy the argument.
IN this case:
Premise 1) angle > 90 => obtuse
Premise 2) angle = 102 [i.e. it is true that angle > 90]]
Conclusion: it is true that angle is obtuse
a) ∠PQR=65° (alternate interior angles theorem)
∠PRQ = 60° (linear pair)
x = 55° (angles in a triangle add to 180°)
b) ∠APQ and ∠PQR are congruent alternate interior angles.
