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A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelogram.
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The sides of a triangle DCE are
DC = 15 cm, CE = 13 cm, ED = 14 cm
Let h be the height of parallelogram ABCD
Given,
Perimeter of ΔDCE
2s = DC + CE + ED
`⇒S=1/2(15+13+4)`
`⇒s=1/2(42)`
`⇒s=21cm`
ЁЭР┤ЁЭСЯЁЭСТЁЭСО ЁЭСЬЁЭСУ ΔЁЭР╖ЁЭР╢ЁЭР╕ = `sqrt(s(s-dc)(s-ce)(s-ed))`
`=sqrt(21(21-15)(21-13)(21-14))`
`=sqrt(21xx7xx8xx6)`
`=sqrt(84xx84)`
`84 cm^2`
Given that
Area of ΔЁЭСЩЁЭСТ ЁЭР╖ЁЭР╢ЁЭР╕= ЁЭСОЁЭСЯЁЭСТЁЭСО ЁЭСЬЁЭСУ ЁЭР┤ЁЭР╡ЁЭР╢ЁЭР╖
= Area of parallelogram ABCD = =`84cm^2`
⇒ 24×тДО=84 [∴ Area of parallelogram = base × height]
⇒ h = 6 cm
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