the area of a square is equal to the area of a rectangle whose are 16cm and 9cm.find the perimeter of a square also find the ratio of the length of the diagonal of the square and the rectangle .
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Answer:
given,
length of rectangle is 16cm
breadth of rectangle is 9cm
then area of rectangle=16x9=144cm^2
given, area of rectangle= area of square
then area of square= 144cm^2
let one side of square is a,
then area of square is a^2=144
then. a= √ 144= 12
i.e side of square is 12cm
perimeter of square is 4a=4x12=48cm
length of diagonal of square is √2a=√2x12=12√2cm=16.97....cm ---1
length of diagonal of rectangle=√((16)^2+(9)^2)=18.35..cm ----2
asked.equation 1/2. =16.97/18.35 =0.924
therefore ratio of length of diagonal of square to rectangle is 0.924...
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