A triangular road sign has a height of 3 feet and a base of 2.5 feet. How much larger in area is this sign than one with a height of 2.5 feet and a base of 3 feet?

Not larger or smaller; the areas are the same

Step-by-step explanation:

Recall that the formula for the area of a triangle of base b and height h is

A = (1/2)(b)(h).

In the first case, h = 3 ft and b = 2.5 ft.  This results in an area of 3.75 ft^2.

In the second case, h = 2.5 ft and b = 3 ft.  The area is the same:  3.75 ft^2.

This is because A = (1/2)(b)(h) has the same value regardless of the order in which b and h  are used as multipliers.

There is no difference in the areas of the two signs.  The areas are the same.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

answer: 10 meter

step-by-step explanation:

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