The figure represents a rectangle with a trinagle inside.
Find the ratio between the white area and the grey area.
Find the ratio between the white area and the grey area.
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- Triangle inside a rectangle
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Triangle inside a rectangle
Source: Beat The GMAT — Problem Solving |
Area of a rect = l * b
Area of white triangls = 1/2 base * ht
if u notice base = l and ht = b
say l = 4 and b = 2
area of grey = area of rect - area of white triangle
= 8 - 4 = 4
Ratio = white/grey = 4/4 = 1
Area of white triangls = 1/2 base * ht
if u notice base = l and ht = b
say l = 4 and b = 2
area of grey = area of rect - area of white triangle
= 8 - 4 = 4
Ratio = white/grey = 4/4 = 1
"if a trinagle and a parallelogram lie on the same base and between the same parallel lines then area of tringale is half of area of parallelogram"
this is true of rectangle too
this is true of rectangle too
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There are a few ways to see that the ratio is 1:1, including a couple of good ways in the above posts. You could also do as follows:
-draw a vertical line from the top corner of the white triangle to the bottom of the rectangle. This divides the large rectangle into two smaller rectangles, and each is clearly half-white, half-shaded, since the edge of the white triangle is a diagonal of each smaller rectangle.
-draw a vertical line from the top corner of the white triangle to the bottom of the rectangle. This divides the large rectangle into two smaller rectangles, and each is clearly half-white, half-shaded, since the edge of the white triangle is a diagonal of each smaller rectangle.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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