Answer:
Step-by-step explanation:
To prove that this triangle is a right triangle, we need to check the side lengths using pythogoras theorem.
Given:
- Longest side = 25 units
- Triangle side lengths: 25, 15x, and 20x
Putting the side lengths into pythogoras theorem:
- ⇒ [tex]25^{2} = 15^{2} + 20^{2}[/tex]
- ⇒ [tex]625 = (10x + 5x)^{2} + (20x + 0x)^{2}[/tex]
Using the formula "(a + b)² = a² + 2ab + b²
- ⇒ [tex]625 =[(10x)^{2} + 2(10x)(5x) + (5x)^{2} ] + [(20x)^{2} + 2(20x)(0) + (0)^{2} ][/tex]
- ⇒ [tex]625 = [(10x)(10x) + 2(10x)(5x) + (5x)(5x)] + [(20x)(20x)][/tex]
- ⇒ [tex]625 =[100x^{2} + 100x^{2} + 25x^{2} ] + [400x^{2} ][/tex]
- ⇒ [tex]625 = 100x^{2} + 100x^{2} + 25x^{2} + 400x^{2}[/tex]
- ⇒ [tex]625 = 625x^{2}[/tex]
Divide both sides by 625:
- ⇒ [tex]\frac{625}{625} = \frac{625x^{2}}{625}[/tex]
- ⇒ [tex]1 = x^{2}[/tex]
- ⇒ [tex]\sqrt{1} = \sqrt{x^{2} }[/tex]
- ⇒ [tex]\sqrt{1 \times 1} = \sqrt{x \times x }[/tex]
- ⇒ [tex]1 = x[/tex]
The value of x that proves this triangle a right triangle is 1.
