SOLUTION: (57) The diagonal of a square has length 7. Find the perimeter of a square with twice the area.

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Question 1209527: (57) The diagonal of a square has length 7. Find the perimeter of a square with twice the area.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39615) About Me  (Show Source):
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The diagonal of a square has length 7.
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x by x dimensions.
x%5E2%2Bx%5E2=7%5E2, simple 45-45-90 right triangle
2x%5E2=49
x=7%2Fsqrt%282%29
the area is
49%2F2


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Find the perimeter of a square with twice the area.
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TWICE the area of the first square is 49.
The square having area of 49 square units is of some side length m
m%5E2=49,
m=7
Perimeter of this square is then 4m=4%2A7=highlight%2828%29.

Answer by ikleyn(52767) About Me  (Show Source):
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If the diagonal of the square is 7 units long,  it means that the side length is  7%2Fsqrt%282%29 units long.

Then the area of this square is  %287%2Fsqrt%282%29%29%5E2 = 49%2F2  square units.


Then the doubled area is  49  square units.


Then the side of the greater square is  sqrt%2849%29 = 7 units.


Then the perimeter of the greater square is 4*7 = 28 units.    ANSWER

Solved.