SOLUTION: There's two squares. Ones bigger than the other. The area of the bigger square is twice the area of the smaller. The total perimeter of the squares together is 16 inches. What's th

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Question 740620: There's two squares. Ones bigger than the other. The area of the bigger square is twice the area of the smaller. The total perimeter of the squares together is 16 inches. What's the side lengths of the larger square?
Found 3 solutions by lynnlo, josmiceli, stanbon:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the side of the bigger square
Let +t+ = the side of the smaller square
The area of the bigger square is +s%5E2+
The area of the smaller square is +t%5E2+
given:
(1) +s%5E2+=+2t%5E2+
(2) +4s+%2B+4t+=+16+ in
-------------------
(2) +s+%2B+t+=+4+
(2) +t+=+4+-+s+
Substitute (2) into (1)
(1) +s%5E2+=+2%2A%28+4-s+%29%5E2+
(1) +s%5E2+=+2%2A%28+16+-+8s+%2B+s%5E2+%29+
(1) +s%5E2+=+32+-+16s+%2B+2s%5E2+
(1) +s%5E2+-+16s+%2B+32+=+0+
Use the quadratic formula
+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-16+
+c+=+32+
+s+=+%28-%28-16%29+%2B-+sqrt%28+%28-16%29%5E2+-+4%2A1%2A32+%29%29+%2F+%282%2A1%29+
+s+=+%28+16+%2B-+sqrt%28+256++-+128+%29%29+%2F+2+
+s+=+%28+16+%2B-+sqrt%28+128+%29%29+%2F+2+
+s+=+%28+16+%2B-+sqrt%28+2%2A64+%29%29+%2F+2+
+s+=+%28+16+%2B-+8%2Asqrt%28+2+%29%29+%2F+2+
+s+=+%28+8+%2B+4%2A1.414+%29+
+s+=+8+%2B+5.656+
+s+=+13.656+ ( this result must be discarded, since it's greater than 4 )
and
+s+=+%28+8+-+5.656+%29+
+s+=+2.344+
----------------
and,
+t+=+4+-+s+
+t+=+4+-+2.344+
+t+=+1.656+
--------------
The side of the larger square is 2.344 inches
check:
(1) +s%5E2+=+2t%5E2+
(1) +2.344%5E2+=+2%2A1.656%5E2+
(1) +5.494+=+2%2A2.742+
(1) +5.494+=+5.485+
This is off a little too much- If you redo the
math to another decimal place, I think it will
come out right


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
There's two squares. Ones bigger than the other. The area of the bigger square is twice the area of the smaller. The total perimeter of the squares together is 16 inches. What's the side lengths of the larger square?
--------
Smaller Square:
Area = 4x^2 ; side = 2x ; Perimeter = 4*2x = 8x
----
Larger Square:
Area = 8x^2 ; side = 2^(3/2)x ; Perimeter = 4*2^(3/2)x = 2^(7/2)x
------
Equation:
Sum of Perimeters = 16
-----
8x + 2^(7/2)x = 16
(8+8sqrt(2))x = 16
19.313x = 16
x = 0.8284 inches
------
Smaller side length = 2x = 1.657
Larger side length = 2^(3/2)x = 2.3431
============
Cheers,
Stan H.
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