Math Problem Statement

The length of the sides of a right-angled triangle is (2x + 1) cm and x cm. Find x if 2x + 1 is the hypotenuse.

Solution

The problem you've uploaded reads:

The length of the sides of a right-angled triangle is (2x+1)(2x + 1) cm and xx cm. Find xx if 2x+12x + 1 is the hypotenuse.

We can solve this using the Pythagorean theorem, which states:

(hypotenuse)2=(leg 1)2+(leg 2)2\text{(hypotenuse)}^2 = \text{(leg 1)}^2 + \text{(leg 2)}^2

Given:

  • Hypotenuse = 2x+12x + 1
  • One leg = xx
  • Other leg = unknown\text{unknown}

From the problem, it seems we are missing the length of the second leg, but it appears to be one of two standard setups:

  1. If the sides are xx and xx, then both legs are equal to xx.
  2. If the side lengths are xx and something like 2x2x, we would need clarification.

Since you haven't mentioned the second leg clearly, let me know if you'd like to confirm or if the second leg is missing from the image.

I will continue with assumption (1), where both legs are equal, and we can set up the equation:

(2x+1)2=x2+x2(2x + 1)^2 = x^2 + x^2

Let me know if you'd like me to proceed with solving this!

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Math Problem Analysis

Mathematical Concepts

Algebra
Pythagorean Theorem
Quadratic Equations

Formulas

Pythagorean theorem: a² + b² = c²
Quadratic equation formula: ax² + bx + c = 0

Theorems

Pythagorean Theorem
Quadratic Formula

Suitable Grade Level

Grades 8-10