Question

A parallelogram the measures of whose adjacent sides are 28cm and 42cm has one diagonal 38cm. Find the altitude on the side 42 cm

Answer 1

Heya Dear,

                  ______________________________________

Given,

One side ( AB ) = 42 cm

Another ( BC ) = 28 cm

One Diagonal ( AC ) = 38 cm.

We know that diagonal of a parallelogram divides it into two equal parts.

So, Ar. of Parallelogram ABCD = Ar. of ΔABC × 2

For ΔABC,

AB(c) = 42 CM , BC(a) = 28 CM and AC(b) = 38 CM.

Semi perimeter ( s ) =  ( a + b + c ) / 2

                                = ( 42 cm + 28 cm + 38 cm ) / 2

                                = ( 108 cm ) / 2

                               = 54 cm.

Now,

⇒ ( s - a ) =  54 cm - 28 cm = 26 cm

⇒ ( s - b ) = 54 cm - 38 cm = 16 cm

⇒ ( s - c ) = 54 cm - 42 cm = 12 cm.

By Heron's Formula ,

Ar. of ΔABC = √{ s ( s - a ) ( s - b ) ( s -c ) }

                    = √ ( 54 cm × 12 cm × 16 cm × 26 cm ) 

                    = √ ( 2 × 3³ × 2² × 3 × 2⁴ × 2 × 13 cm⁴ )

                   = √ ( 3⁴ × 2⁸ × 13 cm⁴ )

                   = 3² × 2⁴ cm² √13

                   = 144√13 cm²

Now,

⇒ Ar. of parallelogram ABCD = 2 × Ar. of Δ ABC

                                               = 2 × 144√13 cm²

                                              = 288√13 cm².

⇒ Ar. of a Parallelogram = Base × Corresponding altitude

⇒ 288√13 cm² = 42 cm × DE

⇒ DE = 288√13 cm² ÷ 42

⇒ DE = 48√13 cm² / 7

∴ DE = 48√13 cm² / 7.

Hope it helps !

Answer 2

Answer:

The answer is 48root17/19