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# A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

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CBSE/Class 9/Mathematics/Unit 5-Mensuration/Heron's formula/NCERT Solutions/Exercise 12.2

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For triangle Perimeter of triangle = (26 + 28 + 30) cm = 84 cm 2s = 84 cm s = 42 cm By Heron’s formula, Area of triangle Area of triangle = 336 cm2 Let the height of the parallelogram be h. Area of parallelogram = Area of triangle h × 28 cm = 336 cm2 h = 12 cm Therefore, the height of the... read more

For triangle

Perimeter of triangle = (26 + 28 + 30) cm = 84 cm

2s = 84 cm

s = 42 cm

By Heron’s formula,

Area of triangle

Area of triangle

= 336 cm2

Let the height of the parallelogram be h.

Area of parallelogram = Area of triangle

h × 28 cm = 336 cm2

h = 12 cm

Therefore, the height of the parallelogram is 12 cm.

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The area of the triangle = √42 ( 42 - 26 ) ( 42 - 28 ) ( 42 - 30 ) = √ 42 × 16 × 14 × 12 = √ 2 × 3 × 7 × 4 × 4 × 7 × 2 × 4 × 3 = 2 × 3 × 7 × 4 × 2 = 336cm². Let h be the height of the parallelogram. ∴... read more

The area of the triangle

= √42 ( 42 - 26 ) ( 42 - 28 ) ( 42 - 30 )

= √ 42 × 16 × 14 × 12

= √ 2 × 3 × 7 × 4 × 4 × 7 × 2 × 4 × 3

= 2 × 3 × 7 × 4 × 2 = 336cm².

Let h be the height of the parallelogram.

∴ area of the parallelogram = bh

= 28cm × h .

Also, area of the triangle = area of the parallelogram.

∴ 28h = 336 ∴ h = 336/28 = 12.

∴ height of the parallelogram = 12cm.

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12cm
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Since the 3 sides for the triangle are known and the area of both are equal. SO area of triangle using Heron's Formula is Sq. root ( 42*16*14*12) = 336 [ where s = (26+28+30)/2 = 42 Now area of parallologram = Base * Height 336 = 28* height Height = 12 read more

Since the 3 sides for the triangle are known and the area of both are equal. SO area of triangle using Heron's Formula is Sq. root ( 42*16*14*12) = 336 [ where s = (26+28+30)/2 = 42

Now area of parallologram = Base * Height

336 = 28* height

Height = 12

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6cm
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Mca Certified Home/Online Tutor With 12 Years Experience.

First find the area of triangle which will be 336sq metre. Triangle and ||gm having same base will be equal in area so Area of ||gm= 336square meter Base=28meter Ar of ||gm = base × Height 336=28x height Height = 12cm
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12 cm.
Comments

Use herons formula to find area of triangle.it is168 sqcm. 168=28×height Height=168/28=6cm
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Height :12 cm
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