Answer:
shown in explanation
Step-by-step explanation:
a) ∆EPB similar to ∆ERG
b) angle BEP = angle GER (common angle shared)
angle EPB = angle ERG (corresponding angles, PB//RG, parallelogram)
therefore through Angle-Angle similarity test, ∆EPB is similar to ∆ERG
or explanation can also be shortened to
∆EPB is similar to ∆ERG (AA, similarity)
c) since proven they are similar ∆, then we can proceed to use property of ratio of corresponding sides being equal
![\frac{pb}{rg} = \frac{ep}{er}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bpb%7D%7Brg%7D%20%20%3D%20%20%5Cfrac%7Bep%7D%7Ber%7D%20)
RG = 200+300=500m
![\frac{200}{500} = \frac{ep}{ep + 350}](https://tex.z-dn.net/?f=%20%5Cfrac%7B200%7D%7B500%7D%20%20%3D%20%20%5Cfrac%7Bep%7D%7Bep%20%2B%20350%7D%20)
cross multiply (from what I've learnt)
2ep+700=5ep
ep= 700/3 = 233 ⅓m (answer for length EP)
Do the same for length BE(using ratio of corresponding sides)
![\frac{be}{ge} = \frac{pb}{rg}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bbe%7D%7Bge%7D%20%20%3D%20%20%5Cfrac%7Bpb%7D%7Brg%7D%20)
![\frac{be}{be + 400} = \frac{200}{500}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bbe%7D%7Bbe%20%2B%20400%7D%20%20%3D%20%20%5Cfrac%7B200%7D%7B500%7D%20)
cross multiply again to get:
5BE = 2BE + 800
BE = 800/3 = 266 ⅔ m (answer for length BE)
V=pie r square h/3
Hope you get the picture!
X is equal to 440
440/8=55