Question

midterm cumulative test
gina has designed two triangular flower beds, as shown below.
which statement is true for the two flower beds?
they have the same perimeter.
the length of side pq is equal to 10 feet.
they have different areas.
the length of side bc is equal to 10 feet.

Explanation:

Step1: Analyze triangle - congruence concepts

We are not given enough information to say the triangles are congruent. But we can use basic triangle - side and area knowledge.

Step2: Consider perimeter

Without knowing all side - lengths, we can't say perimeters are equal.

Step3: Consider side - length equality

Since we have no information about congruence or specific side - length relationships other than one side of each triangle being 10 feet, we can't say BC = 10 feet or PQ = 10 feet.

Step4: Consider area

The area of a triangle is given by $A=\frac{1}{2}bh$. Without knowing base and height values for each triangle, we can't say for sure if areas are different. But if we assume non - congruent triangles with no special relationships, we can't claim same area.
However, if we consider the fact that we know one side of each triangle is 10 feet and no information about congruence, we note that we have no basis to say perimeters are equal, no way to determine other side - lengths exactly. But if we assume non - congruent triangles, we can't claim they have the same area. And since no congruence is given, we can't say BC = 10 or PQ = 10. The most reasonable option is that we have no way to determine equality of perimeters or specific side - lengths without more information, and we can assume non - congruent triangles have different areas in the absence of further details.

Answer:

They have different areas.