Question

the areas of two squares are in the ratio to 225 : 256 what is the ratio of their perimeters

Answer 1

Answer:    15:16

Step-by-step explanation:

Let the side of square 1 be "a"and the square 2 be ''b"

                                    Given  $\frac{a^{2} }{b^{2}}$=$\frac{225}{256}$

                          Square rooting on both sides

                                           $\frac{a}{b}$=$\frac{15}{16}$

   Perimeter of square is 4 times its side so the required ratio is 4a:4b

                           which is a:b = 15:16

Answer 2

Let the area of 1st and 2nd squares be
${s1}^{2} \: \: and \: \: \: \: {s2}^{2} \: \: \: \: then \\ \\ \frac{{s1}^{2}}{{s2}^{2}} = \frac{225}{256} \\ \\ \\ \frac{s1}{s2} = \sqrt{ \frac{225}{256} } \\ \\ \frac{s1}{s2} = \frac{15}{16} \\ \\ \\ let \: the \: sides \: of \: the \: squares \: be \: s1 \: s2 \\ then \\ \\ ratio \: of \: perimeter \\ \\ = \frac{4(s1)}{4(s2)} = \frac{4 \times 15}{4 \times 16} \\ \\ = \frac{60}{64 } or \frac{15}{16}$







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