Mathematics 10 — Exercise 7.3 · Q1 (ii)

Full question

A triangular prism has FE = 5 cm, EC = 4 cm and BC = 3 cm, as shown in the diagram. Find BF.

Step-by-step solution

1. Use right triangle BCF: BF²=BC²+CF².

   $$\mathrm{BF²}=3^2+41$$

2. Square 3 to get 9, then add 41: 9+41=50.

3. Extract a perfect-square factor from under the root.

   $$50=25\times 2$$

4. Take the square root and simplify √50=5√2.

   $$\sqrt{50}=5\times \sqrt{2}$$

Answer

The final answer is shown below.