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The figure shows two triangles?
The figure shows two rectangles with one (GHJK) fitting inside of the other (LMNO).The rectangle labeled GHJK is shaded in. In the figure above, LMNO and GHJK are rectangles where GH=1/2LM and HJ=1/2MN. What fraction of the region bounded by LMNO is not shaded?
If I assign the width, GH, of the inner triangle to be 1, and assign the length HJ of the inner rectangle to be 2, then I get a ratio of 4:1.
But would that be correct? I think the right answer would be that 3/4 of the area of the larger rectangle is not shaded.
1 Answer
- 8 years agoFavorite Answer
Area of a rectangle = length * breadth
Area of the rectangle LMNO = LM * MN
Area of the rectangle GHJK = GH * JK
=( (1/2)LM )* ((1/2)*MN)
= 1/4*LM*MN
area of unshaded region = area of LMNO - area of the shaded region
= LMNO - GHJK
= LMNO - 1/4*LMNO
= 3/4* LMNO
Therefore the area of unshaded region is 3/4 thu of the total region bounded