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Standard IX

Mathematics

Rhombus

Given a recta...

Question

Given a rectangle ABCD and P, Q, R, and S are mid-points of AB, BC, CD, and DA, respectively. If the length of diagonal of a rectangle is 8 cm, find the lengths of all sides of the quadrilateral PQRS.

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Solution

The figure PQRS, formed by joining the mid points of the adjacent sides of a rectangle ABCD is a rhombus.
In $Δ B C D$ , the points Q and R are mid points sides BC and CD respectively.
$∴ Q R | | D B$ (By mid-point theorem)
$Q R = \frac{1}{2} D B$
$Q R = \frac{1}{2} (8)$
$Q R = 4$
Hence, it is rhombus with side 4 cm.

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Given a rectangle ABCD and P, Q, R, and S are mid-points of AB, BC, CD, and DA, respectively. If the length of diagonal of a rectangle is 8 cm, find the lengths of all sides of the quadrilateral PQRS.

The figure PQRS, formed by joining the mid points of the adjacent sides of a rectangle ABCD is a rhombus. In ΔBCD, the points Q and R are mid points sides BC and CD respectively. ∴QR || DB (By mid-point theorem) QR=12DB QR=12(8) QR=4 Hence, it is rhombus with side 4 cm.