Question

A triangle and a parallelogram have the same base and same area. If the side of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stand on the base 28 cm, Find the height of the parallelogram/

Answer 1

Gívєn :-

• Triangle and parallelogram have same base αnd area.
• Sides of triangle - 26, 28, 30cm
• Base of parallelogram - 28cm

Tσ fínd :-

• Height of parallelogram

Sσlutíσn :-

Finding area of triangle -

$\sqrt{s(s-a)(s-b)(s-c)}$

Here,

s = 30 + 28 + 26/2

s = 42

• s = 42
• a = 30
• b = 28
• c = 26

Substituting values in formula :-

→ √42(42-30)(42-28)(42-26)

→ √42 x 12 x 14 x 16

→ √2 x 3 x 7 x 2 x 2 x 3 x 2 x 2 x 2 x 2

→ √2 x 2 x 6 x 6 x 7 x 7 x 16

→ 2 x 4 x 6 x 7

→ 336

Area = 336 cm²

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Area of triangle = 1/2 x b x h

• Base - 28 ( given )
• Height - ?
• Area - 336

Substituting in formula :-

336 = 1/2 x 28 x h

1/28 x 336 = h

h = 12

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It is given that area of triangle and parallelogram is equal therefore, height of parallelogram is also 12 cm

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Vєrífícαtíσn :-

Area of parallelogram - b x h

12 x 28 = 336

Answer 2

Answer:

12 cm

Step-by-step explanation:

Given ;  

Common base = 28 cm

Other two side of triangle are 26 cm and 30 cm.  

In case of parallelogram  

Area of parallelogram = Base × Height  

Let height be h

Area of parallelogram = 28 × h ... ( i )  

In case of triangle  

Area of triangle = √ [ s ( s - a ) ( s - b ) ( s - c )  ]

For s = a + b + c / 2

We have a = 28 , b = 26 and c = 30

s = 28 + 30 + 26 / 2

s = 42 cm

Now Area of triangle = √ [ 42 ( 42 - 28 ) (42 - 30 ) (42 - 26 )  ]

Area of triangle =  √ [ 42  × 12 × 16 × 14 ]

Area of triangle =  √ [ 7 × 6 × 6 × 2 × 2 × 7 × 4 × 4 ]

Area of triangle =   7 × 6 × 4 × 2

Area of triangle =  56 × 6 cm² .

Now we know that area lying in common base in triangle and

parallelogram is equal .

Area of parallelogram = Area of triangle

From ( i )  and ( ii )

28 × h = 56 × 6

h = 2  × 6 cm

h = 12 cm .

Thus the  height of the parallelogram is 12 cm .