Question 2 · The streets of Sadernes
Two chained right triangles: Pythagoras to find two streets and a conversion to paving stones.
Maximum score · 3 pointsIn the village of Sadernes they have decided to add some new streets. For this job they hired a civil engineer, Noa, and an architect, Lluís. A few days ago they began drawing the project map, but before finishing it they lost it among some documents. Now they have found it again and need help to finish it.
The map was going to look like this:
Streets in the figure: Emmy Noether $= 1.6$ km, Antonio Vivaldi $= 1.2$ km, Lise Meitner $= 1.5$ km. Both triangles are right-angled and David Bowie street is the hypotenuse of the lower one and a leg of the upper one.
- What is the length of David Bowie street and Carmina Virgili street? 2 p
- How many paving stones do they need to pave both pavements of Lise Meitner street if each stone is $0.5$ metres long? 1 p
Step-by-step solution
a)
David Bowie is the hypotenuse of the lower triangle, with legs $1.6$ and $1.2$ km. By Pythagoras:
Carmina Virgili is the hypotenuse of the upper triangle, with legs $1.5$ (Lise Meitner) and $2$ km (David Bowie):
b)
The street is $1.5$ km $= 1500$ m long and has two pavements, so $2 \cdot 1500 = 3000$ m of pavement. Each stone covers $0.5$ m: