{"id":37564,"date":"2026-01-06T15:10:11","date_gmt":"2026-01-06T15:10:11","guid":{"rendered":"https:\/\/mp.moonpreneur.com\/math-corner\/?p=37564"},"modified":"2026-01-09T17:14:49","modified_gmt":"2026-01-09T17:14:49","slug":"geometry-problem","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/geometry-problem\/","title":{"rendered":"Interesting Geometry Problem to Solve For Kids"},"content":{"rendered":"\t\t
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Today, we are going to solve a classic geometry problem that even the Gemini of ChatGPT sometimes fails. The trick to solve it is easy, but needs a little bit of attention. Lets look at the Problem.<\/span><\/p>

Find the value of x<\/span><\/h3>

\"\"<\/a><\/p>

Step 1: Find the Missing Link<\/b><\/span><\/h4>

We start with a right-angled triangle with sides of <\/span>24 and 7<\/b>. Your first instinct should always be the Pythagorean theorem!\u00a0<\/span><\/p>

By calculating \\(\\displaystyle \\sqrt{24^{2} + 7^{2}}\\) we get, \\(\\displaystyle \\sqrt{576 + 49}\\) which equals \\(\\displaystyle \\sqrt{625}\\).<\/span><\/p>

So, our first unknown line is <\/span>25.<\/b><\/p>

Recommended Reading: <\/b>An overview of the SAT Math Test Sections<\/b><\/a><\/p>

Step 2: Think Outside the (Semi) Circle<\/b><\/span><\/h4>

Here is where the “magic” happens. To find <\/span>x<\/span><\/i>, the trick is to extend the semicircle into a full circle. By doing this and connecting the lines, we create similar triangles that reveal a much larger right-angled triangle.<\/span><\/p>

\"\"<\/a><\/p>

Recommended eading <\/b>The Ultimate Guide to Solving SAT Quadratics in Seconds<\/span><\/a><\/p>

Step 3: The SAT “Pro-Tip” (The 3-4-5 Trick)<\/b><\/span><\/h4>

In this new, larger triangle, the height is still 24, but the base is now <\/span>7+25<\/span>, giving us <\/span>32<\/b>. Now, you could spend time squaring 32, or you could use a shortcut. Notice that 24 and 32 are both multiples of 8:<\/span><\/p>