A ladder 3.5 M long is placed agamst a perpendicular wall with its foot I metre from the wall. How far up the wall does the ladder reach. If the foot of the ladder is now moved 30 cm further away from the wall how far does the top of the ladder falls.

Let's solve the problem step by step using the Pythagorean theorem. ### **1. Initial Position of the Ladder** - **Given:** - Length of the ladder (\( L \)) = 3.5 meters - Distance from the wall (\( d \)) = 1 meter - **Objective:** - Find the height (\( h \)) the ladder reaches on the wall. - **Using Pythagoras' Theorem:** \[ L^2 = h^2 + d^2 \] \[ h^2 = L^2 - d^2 \] \[ h = \sqrt{3.5^2 - 1^2} = \sqrt{12.25 - 1} = \sqrt{11.25} \approx 3.354 \text{ meters} \] ### **2. After Moving the Foot of the Ladder** - **New Distance from the Wall:** - The foot is moved 30 cm (0.3 meters) further away. - New distance (\( d' \)) = 1 + 0.3 = 1.3 meters - **New Height (\( h' \)):** \[ h'^2 = L^2 - d'^2 \] \[ h' = \sqrt{3.5^2 - 1.3^2} = \sqrt{12.25 - 1.69} = \sqrt{10.56} \approx 3.249 \text{ meters} \] - **Difference in Height:** \[ \Delta h = h - h' \approx 3.354 - 3.249 = 0.105 \text{ meters} \approx 10.5 \text{ centimeters} \] ### **Final Answer** - **Initial Height on the Wall:** Approximately **3.35 meters**. - **After Moving the Foot:** The top of the ladder falls by about **10.5 centimeters**. ### **Summary** 1. The ladder initially reaches approximately **3.35 m** up the wall. 2. After moving the foot 30 cm farther out, the ladder’s top descends by about **10.5 cm**.