Sunday, March 26, 2017

Geometry Problems of the Day

The following problems were taken from the GEOMETRY (COMMON CORE) Regents Exam given on Thursday, January 26, 2017.
Previous problems can be found here.

Part 1

7. The diagram below shows two similar triangles.

If tan O = 3/7, what is the value of x, to the nearest tenth?

(2) 5.6.
tan O = 3/7, and tan O = 2.4/x, so 3/7 = 2.4/x.
3x = (7)(2.4) = 16.8
x = 5.6

8. A farmer has 64 feet of fence to enclose a rectangular vegetable garden. Which dimensions would result in the biggest area for this garden?

(1) the length and the width are equal
A dilation increased the size, so it will no longer be congruent.
For all rectangles with the same perimeter, a square will always have the greatest area.
Consider this:
A square with sides equal to x, will have a perimeter of 4x and area of x2.
A rectangle with sides equal to (x+1) and (x-1), will have a perimeter of 4x and area of x2 - 1.
A rectangle with sides equal to (x+2) and (x-2), will have a perimeter of 4x and area of x2 - 4.
A rectangle with sides equal to (x+3) and (x-3), will have a perimeter of 4x and area of x2 - 9.
etc.
The area will always be some perfect subtracted from x2, which will always be less than x2.




Continue to the next problems.

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