Answer:
Step-by-step explanation:
We have given a parallelogram ABCD.
For a parallelogram,
Opposite pair of sides are parallel to each other.
i.e AD is parallel to BC and AB is parallel to CD.
From the attached figure,
∡1 = ∡4 and ∡2 = ∡3 {If two parallel lines cut by a transversal line then alternate interior angles are congruent }
Next, AC ≅ AC {Reflexive identity}
hence, ΔABC ≅ ΔCDA , By Angle-Side-Angle(ASA) congruent property of triangle.
Therefore, AB = CD and AD = BC {Proved}
Answer:
20 minutes should spend on walking and 30 minutes on running.
Step-by-step explanation:
Let x represents the minutes spent on walking and y represents the minutes spent on running,
∵ He burns 4 cal/min walking and 10 cal/min running,
So, the total calories burnt,
Z = 4x + 10y
Which has to be maximised.
Now, he walks between 10 and 20 min each day,
i.e. 10 < x < 20,
Also, he runs between 30 and 45 min each day,
i.e. 30 < y < 45,
By graphing 10 < x < 20 and 30 < y < 45,
We obtained the vertices of feasible region,
(10, 45), (20, 45), (10, 30) and (20, 30)
At (10, 45),
Z = 4(10) + 10(45) = 40 + 450 = 490,
At (20, 45),
Z = 4(20) + 10(45) = 80 + 450 = 530,
At (10, 30),
Z = 4(10) + 10(30) = 40 + 300 = 340,
At (20, 30)
Z = 4(20) + 10(30) = 80 + 300 = 380
Hence, maximum calories is 530 when 20 minutes spent on walking and 30 minutes spent on running.
