Is this true or false? Two similar hexagons have area 36 square inches and 64 square inches. The ratio of a pair of corresponding sides is 9/16.
false,
you should be able to tell me why it is false
To determine whether the statement is true or false, we need to compare the given information about the hexagons.
First, let's recall the properties of similar figures. Similar figures have the same shape but not necessarily the same size. The corresponding sides of similar figures are proportional, meaning that the ratio of the lengths of corresponding sides of two similar figures is constant.
Given:
- Two similar hexagons have area 36 square inches and 64 square inches.
- The ratio of a pair of corresponding sides is 9/16.
To find out if the statement is true, we need to check if the ratio of the areas matches the ratio of the square of the corresponding sides.
Let's calculate the area ratio:
The area ratio is the square of the corresponding side ratio.
Given ratio of corresponding sides: 9/16
Squared ratio of corresponding sides: (9/16)^2 = 81/256
Now, let's check if the area ratio matches:
The first hexagon has an area of 36 square inches. If we multiply 36 by the area ratio, we would expect to get the area of the second hexagon (64 square inches) if the statement is true.
36 * (81/256) = 11.25
The result (11.25) does not match the area of the second hexagon (64 square inches). Thus, the statement is false.
To summarize, two similar hexagons cannot have area 36 square inches and 64 square inches with a corresponding side ratio of 9/16.