the length of one of the diagonal of rhombus is 40 cm if each side of the Rhombus measure 25 CM then what is the length of the diagonals
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Let ABCD is a rhombus , in which AB and CD are it's two diagonals.
Let AB = 40 cm.
AD = AC = BC = BD = 25 cm.
OA = 1/2 × AB = 1/2 × 40 = 20 cm.
In right Angle triangle OAD ,
OA = 20 cm and AD = 25 cm .
By Pythagoras theroem,
AD² = OA² + OD²
OD² = (AD)² - (OA)²
OD² = (25)² - (20)²
OD² = 225.
OD = √225
OD = 15 cm.
CD = 2 × OD = 2 × 15 = 30 cm.
Hence,
Length of other diagonal = 30 cm.
Let AB = 40 cm.
AD = AC = BC = BD = 25 cm.
OA = 1/2 × AB = 1/2 × 40 = 20 cm.
In right Angle triangle OAD ,
OA = 20 cm and AD = 25 cm .
By Pythagoras theroem,
AD² = OA² + OD²
OD² = (AD)² - (OA)²
OD² = (25)² - (20)²
OD² = 225.
OD = √225
OD = 15 cm.
CD = 2 × OD = 2 × 15 = 30 cm.
Hence,
Length of other diagonal = 30 cm.
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30CM
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