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4) Area of rectangle \( =21 \) (4) Now, find the area of the triangle. (1) Area of triangle \( =2 \) square \( A=\frac{1}{2} b h \)

Ask by Ford Morrison. in the United States
Jan 23,2025

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Cannot determine the area of the triangle with the given information.

Solución

It seems that there was an issue with solving the equation. Let's try to solve it manually. Given that the area of the rectangle is 21 and the area of the triangle is 2, we can set up the following equation: \[ 21 = 2 \times \text{base} \times \text{height} \] To find the base and height of the triangle, we can rearrange the equation as follows: \[ \text{base} \times \text{height} = \frac{21}{2} \] Now, we need to find the base and height of the triangle. Let's assume the base of the triangle is \( b \) and the height is \( h \). Then, we have: \[ b \times h = \frac{21}{2} \] To find the base and height, we can use the fact that the area of the triangle is 2. Therefore, we have: \[ \frac{1}{2} \times b \times h = 2 \] Simplifying the equation, we get: \[ b \times h = 4 \] Now, we have two equations: \[ b \times h = \frac{21}{2} \] \[ b \times h = 4 \] We can solve these equations simultaneously to find the base and height of the triangle. Solve the equation by following steps: - step0: Solve for \(b\): \(bh=\frac{21}{2}\) - step1: Rewrite the expression: \(hb=\frac{21}{2}\) - step2: Multiply by the reciprocal: \(hb\times \frac{1}{h}=\frac{21}{2}\times \frac{1}{h}\) - step3: Multiply: \(b=\frac{21}{2h}\) It seems that there was an issue with solving the equation. Let's try to solve it manually. We have two equations: \[ b \times h = \frac{21}{2} \] \[ b \times h = 4 \] We can solve these equations simultaneously to find the base and height of the triangle. From the second equation, we have: \[ b \times h = 4 \] Now, we can substitute this value into the first equation: \[ b \times h = \frac{21}{2} \] \[ 4 = \frac{21}{2} \] Solving for \( b \) and \( h \), we get: \[ b = \frac{21}{2h} \] Now, we can substitute this value into the second equation: \[ b \times h = 4 \] \[ \frac{21}{2h} \times h = 4 \] Simplifying the equation, we get: \[ \frac{21}{2} = 4 \] This equation is not true, which means that there is no solution for the base and height of the triangle. Therefore, we cannot find the area of the triangle using the given information.

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Bonus Knowledge

Let's have some fun with the properties of triangles! The formula for the area of a triangle, \( A = \frac{1}{2} b h \), means you need to know the base \( b \) and the height \( h \) of your triangle. For instance, if your base is 4 units and your height is 2 units, plugging those values in gives you \( A = \frac{1}{2} \times 4 \times 2 = 4 \) square units! Now, let's not forget the rectangular fun! The area of a rectangle is found with the formula \( \text{Area} = l \cdot w \) (length times width). If you know one dimension and the area (like 21 square units), you can find the other dimension. If, for example, the length is 7 units, then the width would be \( \frac{21}{7} = 3 \) units! Math is all about uncovering exciting relationships!

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