Question

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Answer 1

Step-by-step explanation:

(1)

Given, three persons step out together.

So, the minimum distance covered by them = LCM of the measures of steps(30,36,40)

Prime factorization of 30 = 2 * 3 * 5

Prime factorization of 36 = 2 * 2 * 3 * 3

Prime factorization of 40 = 2 * 2 * 2 * 5

LCM(30,36,40) = 2 * 2 * 2 * 3 * 3 * 5

                         = 360.

∴ Each person should walk a minimum distance of 360 km in complete steps.

(2)

Given points are A(3,1), B(5,1), C(a,b), D(4,3)

∴ Diagonal of parallelogram bisect each other.

Coordinates of mid-point are:

⇒ (3 + a/2, 1 + b/2) = (5 + 4/2, 1 + 3/2)

⇒ (3 + a/2, 1 + b/2) = (9/2, 4/2)

⇒ (3 + a/2, 1 + b/2) = (9/2, 2).

On comparing both sides, we get

(a)

(3 + a)/2 = 9/2

⇒ 6 + 2a = 18

⇒ 2a = 12

⇒ a = 6

(b)

(1 + b)/2 = 2

⇒ 1 + b = 4

⇒ b = 3

∴ Values of a and b are 6 and 3.

Hope it helps!

Answer 2

$\huge \bold{hey \: there}$

1) To calculate the minimum distance of each person, we need to find the LCM

Now,

Prime factorisation of

➡30=2×3×5

➡36=2×2×3×3

➡40=2×2×2×5

LCM=2×3×2×3×5×2=360 cm

Answer:360 cm

2) Given, A(3,1), B(5,1), C(a,b), D(4,3) are vertices of a parallelogram.

We know that the diagonals of a parallelogram bisect each other. So the coordinates of the midpoints of the diagonals AC and BD will be equal.

Now,

➡(3+a/2)=4+5/2

3+a/2=9/2

➡a=6

➡(b+1/2)=(3+1/2)

b+1/2=2
b+1=4
b=4-1
➡b=3

The values of a and b are 6 and 3.