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Question
In the given figure, points X, Y, Z are the midpoints of side AB, side BC and side AC of ΔABC respectively. AB = 5 cm, AC = 9 cm and BC = 11 cm. Find the length of XY, YZ, XZ.
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Solution
AB = 5 cm, AC = 9 cm and BC = 11 cm …(Given)
In ∆ABC,
Points X and Y are the midpoints of sides AB and BC respectively. ...(Given)
∴ XY = `1/2` AC ...(From midpoint theorem)
∴ XY = `1/2xx 9`
∴ XY = 4.5 cm
In ∆ABC,
Points Y and Z are the midpoints of sides BC and AC respectively. ...(Given)
∴ YZ = `1/2` AB ...(From midpoint theorem)
∴ YZ = `1/2xx 5`
∴ YZ = 2.5 cm
In ∆ABC,
Points X and Z are the midpoints of lines AB and AC respectively. ...(Given)
∴ XZ = `1/2` BC ...(From midpoint theorem)
∴ XZ = `1/2xx 11`
∴ XZ = 5.5 cm
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