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Question

A rhombus and a square have the same base. If the diagonals of the rhombus measure 30cm and 16cm, respectively, find the area of the square.

A
225cm2
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B
200cm2
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C
240cm2
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D
289cm2
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Solution

The correct option is D 289cm2
In a rhombus, the diagonals bisect each other at 900
Referring the diagram, if PR=30cm,SQ=16cm, then OP=15cm,OQ=8cm
Since POQ is a right angled triangle,
PQ2=OP2+OQ2
=>152+82=289
=>PQ=289=17 cm
Hence, the length of the sides of the rhombus =17 cm.

Given, side of the square = side of rhombus =17cm
Area of square side2=289cm2

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