Two triangles are similar with sides in the ratio 4:9. If the area of the smaller triangle is 64 ext cm2, find the area of the larger triangle. Define the term circle and state the relationship betwee

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Two triangles are similar with sides in the ratio $4:9$. If the area of the smaller triangle is $64 \text{ cm}^2$, find the area of the larger triangle.

Step 1: Understand the relationship between the ratio of sides and the ratio of areas for similar triangles.
If the ratio of corresponding sides of two similar triangles is $a:b$, then the ratio of their areas is $a^2:b^2$.
Given ratio of sides (smaller to larger) is $4:9$.
So, the ratio of their areas (smaller to larger) is $4^2:9^2 = 16:81$.

Step 2: Set up a proportion using the given area.
Let $A_S$ be the area of the smaller triangle and $A_L$ be the area of the larger triangle.

$$\frac{A_S}{A_L} = \frac{16}{81}$$

We are given $A_S = 64 \text{ cm}^2$.

$$\frac{64 \text{ cm}^2}{A_L} = \frac{16}{81}$$

Step 3: Solve for $A_L$.

$$A_L = \frac{64 \text{ cm}^2 \times 81}{16}$$ $$A_L = 4 \text{ cm}^2 \times 81$$ $$A_L = \boxed{\text{324 cm}^2}$$

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Define the term circle and state the relationship between radius and diameter.

A circle is a set of all points in a plane that are equidistant from a fixed point called the center. The radius ($r$) is the distance from the center to any point on the circle. The diameter ($D$) is the distance across the circle passing through its center. The relationship is that the diameter is twice the radius, or $D = 2r$.

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Find the circumference of a Circle with a radius of $7 \text{ cm}$. ($\pi = \frac{22}{7}$)

Step 1: Write the formula for the circumference of a circle.

$$C = 2\pi r$$

Step 2: Substitute the given values.
Given $r = 7 \text{ cm}$ and $\pi = \frac{22}{7}$.

$$C = 2 \times \frac{22}{7} \times 7 \text{ cm}$$

Step 3: Calculate the circumference.

$$C = 2 \times 22 \text{ cm}$$ $$C = \boxed{\text{44 cm}}$$

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Calculate the area of the following use $\pi = \frac{22}{7}$.