Question 1122021: Please help me solve this equation:
Find the dimensions of a rectangle whose area is 270 cm2 and whose perimeter is 66 cm. (Enter your answers as a comma-separated list.)
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
Let me show you a quick, elegant and unexpected method of solving such problems.
You are given that the perimeter of the rectangle is 66 cm; hence, the sum of the length and the width is one half of that:
x + y = 33, where x is the length, and y is the width.
Then the average of the length and the width is one half of 22, i.e. 16.5.
It is clear that the values of x and y are remoted at the same value/distance "u" from the average of 16.5, so we can write
x = 16.5 + u,
y = 16.5 - u.
Then the area is xy = (16.5+u)*(16.5-u) =  , and it is equal to 270, according to the condition.
Hence, = 270, which gives  = 272.25 - 270 = 2.25, and then u =  = 1.5.
Thus the length is x = 16.5 + u = 16.5 + 1.5 = 18,
and the width is x = 16.5 - u = 16.5 - 1.5 = 15.
Answer. The dimensions of the rectangle are 15 cm and 18 cm.
Solved.
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See the lesson
- Three methods to find the dimensions of a rectangle when its perimeter and the area are given
in this site.
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