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Question
A triangle and a parallelogram have the same base and the same area. If the side of the triangle is 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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Solution
Let the sides of the triangle be
a = 26 cm, b = 28 cm and c = 30 cm
Now,
semi-perimeter of a triangle,
s = `( a + b + c )/( 2 ) = ( 26 + 28 + 30 )/(2 )= (84)/(2) = 42 cm`
∴ Area of triangle = `sqrt (s( s - a )( s - b )(s -c ))`
= `sqrt (42( 42 - 26 ) ( 42 - 28 ) (42 - 30 ))`
= `sqrt ( 42 xx 16 xx 14 xx 12 )`
= `sqrt( 7 xx 6 xx 4 xx 4 xx 7 xx 2 xx 6 xx 2)`
= `sqrt( 7 xx 7 xx 4 xx 4 xx 6 xx 6xx 2xx 2)`
= 7 x 4 x 6 x 2
= 336 cm2
Base of a parallelogram = 28 cm
Given ,
Area of parallelogram = Area of triangle
⇒ Base x Height = 336
⇒ 28 x Height = 336
⇒ Height = 12 cm
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