What is the missing numerator? four fifths minus blank over nine equals six forty fifths
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Check the picture below.
now, let's recall that running a segment from a midpoint across to a midpoint in a triangle, creates a midsegment, and a midsegment which is parallel to the "base" of the triangle, is always half of that base.
now, noticing the picture on the top-left triangle, we know those points are midpoints, so those in red are midsegments and therefore half the base, to make it short
IC = HE/2 = 7
JB = IC/2 = 3.5
now onto the top-right triangle, which is the same thing just basing itself on its other end
CG = AH/2 = 10
DF = CG/2 = 5
now, let's go to the picture on the bottom-center
we know that DG = 4, and since D and G are midpoints, DG is the midsegment of CEH thus
CH = 2DG = 8
likewise, on the green triangle ACH, the midsegment IB is half of the base CH, we know CH = 8, so IB = 4.
A diagram helps.
Diagonal TO divides the rectangle into two triangles of base 10 and height 4. The area of the two of them together (the area of the rectangle) is 10*4 = 40.
The area of rectangle TYOC is 40 square units.
Diagonal TO divides the rectangle into two triangles of base 10 and height 4. The area of the two of them together (the area of the rectangle) is 10*4 = 40.
The area of rectangle TYOC is 40 square units.