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Mathematics

1 answer:

krek1111 [17]1 year ago

3 0

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

$\frac{pb}{rg} = \frac{ep}{er}$

RG = 200+300=500m

$\frac{200}{500} = \frac{ep}{ep + 350}$

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)

$\frac{be}{ge} = \frac{pb}{rg}$

$\frac{be}{be + 400} = \frac{200}{500}$

cross multiply again to get:

5BE = 2BE + 800

BE = 800/3 = 266 ⅔ m (answer for length BE)

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Hope this helped!