Question
he two triangles below are similar (but not drawn to scale). Find the value of x . Round answer to the nearest tenth.
ONE IS 32.6IN AND 28.2. TWO IS XAND 17IN
ONE IS 32.6IN AND 28.2. TWO IS XAND 17IN
Answers
Answered by
GPT-4o mini
Since the triangles are similar, the ratios of their corresponding sides are equal. This can be expressed in the following equation:
\[
\frac{32.6}{x} = \frac{28.2}{17}
\]
To solve for \(x\), we can cross-multiply:
\[
32.6 \cdot 17 = 28.2 \cdot x
\]
Calculating \(32.6 \cdot 17\):
\[
32.6 \cdot 17 = 554.2
\]
Now the equation is:
\[
554.2 = 28.2 \cdot x
\]
Next, divide both sides by \(28.2\) to solve for \(x\):
\[
x = \frac{554.2}{28.2}
\]
Calculating this gives:
\[
x \approx 19.6
\]
Rounding to the nearest tenth, the value of \(x\) is:
\[
\boxed{19.6}
\]
\[
\frac{32.6}{x} = \frac{28.2}{17}
\]
To solve for \(x\), we can cross-multiply:
\[
32.6 \cdot 17 = 28.2 \cdot x
\]
Calculating \(32.6 \cdot 17\):
\[
32.6 \cdot 17 = 554.2
\]
Now the equation is:
\[
554.2 = 28.2 \cdot x
\]
Next, divide both sides by \(28.2\) to solve for \(x\):
\[
x = \frac{554.2}{28.2}
\]
Calculating this gives:
\[
x \approx 19.6
\]
Rounding to the nearest tenth, the value of \(x\) is:
\[
\boxed{19.6}
\]
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