1. **Stating the problem:** Calculate the unknown height $x$ in triangle 3 and the unknown side $x$ in triangle 4 using the area formulas. 2. **Triangle 3:** Given sides: base $= 25$ m, height $= x$, and side $= 5$ m (assuming $5$ m is the other leg or height). The area formula is: $$S = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 25 \times x$$ Since the area is not given, we need to find $x$ in terms of area or use Pythagoras if possible. But no area is given, so we assume the area is calculated from the other sides. Using Pythagoras theorem for right triangle: $$x = \sqrt{5^2 + 16^2} = \sqrt{25 + 256} = \sqrt{281}$$ So, $$x = \sqrt{281} \approx 16.76 \text{ m}$$ 3. **Triangle 4:** Given sides: $5\sqrt{2}$ dm, $4$ dm, $6$ dm, $5$ dm, and unknown $x$. Assuming the triangle with legs $4$ dm and $x$ dm, and area $S_2$ is: Area formula: $$S = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times x = 2x$$ If the area $S_2$ is known or can be calculated from other sides, for example, if $S_2 = 10$ dm² (hypothetical), then: $$2x = 10 \Rightarrow x = 5$$ Since no area is given, we use Pythagoras theorem if $x$ is a leg: If $x$ is the hypotenuse or leg, use: $$x = \sqrt{(5\sqrt{2})^2 + 4^2} = \sqrt{50 + 16} = \sqrt{66} \approx 8.12 \text{ dm}$$ **Final answers:** Triangle 3: $x = \sqrt{281} \approx 16.76$ m Triangle 4: $x = \sqrt{66} \approx 8.12$ dm