a.
To find: The ratio of theareas of region I to that of region II.
a.

Answer to Problem 28RP
The ratio of the area of region I to that of region II is 16:81.
Explanation of Solution
Given Information:
Sides of the quadrilateral are
Formula used:
Ratio of areas of two similar
Calculation:
Sides of the quadrilateral
Let the diagonals intersect at point
In
As we know that, the ratio of areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.
Hence, ratio of the area of region I to that of region II is 16:81.
b.
To find: The ratio of the areas of triangle I to that of triangle II.
b.

Answer to Problem 28RP
The ratio of the area of region I to that of region II is 49:81.
Explanation of Solution
Given Information:
Sides of the triangle I are
Sides of the triangle II are
Formula used:
Ratio of areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.
Calculation:
Sides of the triangle I are
Sides of the triangle II are
Let the triangles intersect at point
In
As we know that, the ratio of areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.
Hence, ratio of the area of region I to that of region II is 49:81.
c.
To calculate: The ratio of the areas of the two triangles.
c.

Answer to Problem 28RP
The ratio of the area of region I to that of region II is 1:!.
Explanation of Solution
Given Information:
Sides of the triangle I are
One side of the triangle II is
Two
Formula used:
Ratio of areas of two congruent triangle is equal to 1:1.
Calculation:
Sides of the triangle I are
One side of the triangle II is
In
As the triangles are congruent, so the triangles will have equal areas.
Hence, the ratio of the area of region I to that of region II is 1:1.
Chapter 11 Solutions
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