Math / Geometry

QuestionSimilarityProportions K Find the value ark $2

Studdy Solution

STEP 1

What is this asking? We've got two similar triangles, and we need to find the mystery value $x$ by comparing their corresponding sides! Watch out! Don't mix up which sides match up between the triangles!
Also, make sure your final answer makes sense – side lengths can't be negative!

STEP 2

1. Set up the proportion
2. Cross-multiply
3. Solve for $x$
4. Check the solution

STEP 3

Alright, let's set up a proportion using the corresponding sides of the triangles.
The ratio of corresponding sides in similar triangles is equal.
We can write this as a fraction: $\frac{\text{side of big triangle}}{\text{corresponding side of small triangle}}$ .

STEP 4

So, we can match up $x + 2$ from the big triangle with $x$ from the small triangle, and $52$ from the big triangle with $x - 2$ from the small triangle.
This gives us the proportion: $\frac{x + 2}{x} = \frac{52}{x - 2}$

STEP 5

Time to cross-multiply!
We

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