SOLUTION: A piece of twine 48 inches long is cut into two lengths. Each length is then used to form a square. The sum of the areas of the two squares is 74 square inches. Find the length of
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Question 347069: A piece of twine 48 inches long is cut into two lengths. Each length is then used to form a square. The sum of the areas of the two squares is 74 square inches. Find the length of each side of the smaller square and the larger square. Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Let s=one length of twine--------------------perimeter of one square
Then 48-s=the other length---perimeter of second square
Side of first square=s/4; Area=s^2/16
Side of second square=(48-s)/4; Area=(2304-96s+s^2)/16
And we are told that the two areas add up to 74 sq inches, so:
s^2/16+(2304-96s+s^2)/16=74 multiply each term by 16
s^2+2304-96s+s^2=1184 simplify
2s^2-96s+1120=0
s^2-48s+560=0----------quadratic in standard form and it can be factored
(s-28)(s-20)=0
s=28 in--- solution
s=20 in--- -solution
Side of larger square =28/4=7 in; area=49 sq in
Side of smaller square=20/4=5 in; area=25 sq in
49+25=74
74=74
Hope this helps---ptaylor
