What is the area of the following parallelogram in square centimeters?
a) 396 cm2
b) 360 cm2
c) 3.6 cm2
d) 3.96 cm2
which of the following sets of numbers is a pythagorean triple?
a) 42, 40, 82
b) 42, 40, 58
c) 41, 41, 58
d) 40, 41, 57

Answer with explanation:

1.⇒Area of Parallelogram = Corresponding height × Base

                                        = 2 cm × 18 mm

→1 cm = 10 mm

So,  Area of Parallelogram

                                = 2 cm × 1.8 cm

                                 = 3.6 cm²

Option C: →3.6 cm²

→→→2. A triplet ,that is set of three numbers is called Pythagorean triplet, if it is of the form of : {m²-1, 2 m , m²+1}

That is if you write the Pythagorean rule for Right triangle, having sides , m²-1, 2 m , m²+1

then ,→ Square of Largest side = Sum of squares of two smallest side

Square of Largest Side = (m²+1)²

Sum of squares of two smallest side= (2 m)² + (m²-1)²

                  = 4 m² + (m²)² -2 m²+1

                 = (m²)² +2 m²+1

                  =(m²+1)²

So, we will check out , out of four options which of them are Pythagorean Triplet.

Option 1.

Square of Largest Number = 82²=6724

Sum of squares of two smaller number= 42² + 40²

                      = 1764 +1600

                     = 3364

→Square of Largest Number ≠Sum of squares of two smaller number

6724 ≠ 3364

Not a Pythagorean Triple.

Option 2.

Square of Largest Number = 58²=3364

Sum of squares of two smaller number= 42² + 40²

                      = 1764 +1600

                     = 3364

→Square of Largest Number =Sum of squares of two smaller number

3364= 3364

A Pythagorean Triple.

Option 3.

Square of Largest Number = 58²=3364

Sum of squares of two smaller number= 41² + 41²

                      = 1681 +1681

                     = 3362

→Square of Largest Number ≠Sum of squares of two smaller number

3364 ≠ 3362

Not a Pythagorean Triple.

Option 4.

Square of Largest Number = 57²=3249

Sum of squares of two smaller number= 41² + 40²

                      = 1681 +1600

                     = 3281

→Square of Largest Number ≠Sum of squares of two smaller number

3249 ≠ 3281

Not a Pythagorean Triple.

Option B: (42, 40,58) is a Pythagorean triple.

your answer would be 10x - 1