1. **State the problem:** We have two triangles side by side with given side lengths. We need to find the length $x$ of the hypotenuse of the right triangle. 2. **Identify the triangles and given sides:** - Left triangle: base = 77 m, height = 49 m - Right triangle: base = 88 m, hypotenuse = $x$ 3. **Assumption:** The two triangles are similar because they share an angle and their sides are proportional. 4. **Set up the proportion using similarity:** $$\frac{\text{height of left}}{\text{base of left}} = \frac{\text{height of right}}{\text{base of right}}$$ Let the height of the right triangle be $h$. Then: $$\frac{49}{77} = \frac{h}{88}$$ 5. **Solve for $h$:** $$h = \frac{49}{77} \times 88$$ 6. **Calculate $h$:** $$h = \frac{49 \times 88}{77}$$ Simplify by canceling common factors: $$h = \frac{\cancel{49} \times 88}{\cancel{77}} = \frac{7 \times 88}{11}$$ Since $49 = 7 \times 7$ and $77 = 7 \times 11$, canceling one 7: $$h = \frac{7 \times 88}{11} = 7 \times 8 = 56$$ 7. **Use Pythagoras theorem to find $x$:** $$x = \sqrt{(88)^2 + (56)^2}$$ Calculate squares: $$88^2 = 7744, \quad 56^2 = 3136$$ Sum: $$7744 + 3136 = 10880$$ 8. **Calculate $x$:** $$x = \sqrt{10880}$$ Approximate: $$x \approx 104.35$$ **Final answer:** $$x \approx 104.35 \text{ m}$$