The Petpet Supplies shop is 655 metres from the Smoothie Store, 393 Metres from the Defence Magic shop, and 314 metres from the Grooming Parlour. The Defence Magic shop is 236 metres from the Grooming Parlour and 524 metres from the Smoothie Store. Assuming the distance between the Grooming Parlour and the Smoothie Store is less than the distance between the Petpet Supplies shop and the Smoothie Store, what is the distance between the Grooming Parlour and the Smoothie Store? Please round to the nearest metre.

good question.. i know how to cheat.

is it possible to do this without going into angles?

629 meters:confused:

i'm probably out by more than a metre but the working is as follows

 

[hide] label all corners the first letter of each name, you end up with 2 triangles, sharing the line between P and D. there are 2 solutions but a qualifier in the question makes us focus on the one where the triangles overlap.

the angle at D between P and S is about 91.83 degrees

the angle at D between P and G is about 53.03 degrees

so the angle at D between G and S is about 38.8 degrees

use the cosine rule to get the distance between G and S and you end up with a distance of 371 metres [/hide]

CLUE: 655, 393, and 524 is a pythagorian triple

288m?

this isn't one of those stupid Lenny Conundrums from Neopets, is it

Are you assuming straight lines that can pass through the intervening shops etc?

This puzzle is sponsored by the flat earth society.