Question

The 4 cities(A,B,C&D) are to be connected by roads.The budget allows 22 km of road to be build. How can it be done? In the given figure ABCD is a square with each side 8km.​

Answer 1

The roads are 4 km , 4 km, 4 km , 4 km and 6 km.

Explanation:

From the first diagram below, for the 4 cities to be connected all the roads will be 32 km but the budget only allows for 22 km roads. The second diagram demonstrate how you could build a 22 km road that connects the 4 cities.

The square ABCD all the sides are equal. Base on the diagram 2 triangles are formed.

The length of the hypotenuse can be found using Pythagoras formula.

c² = a² + 4²

c² = 16a²

square both sides

c = √16a²

c = 4a

The hypotenuse of the right angle triangles formed are 4a.

The length of the line joining the 2 triangles can be solved as 8 - a - a = 8 - 2a.

Now recall the roads all together is 22 km.

Therefore,

add the hypotenuse of the 4 right angle triangle and 8 - 2a to connect the 4 cities.

4a + 4a + 4a + 4a + 8 -2a = 22

16a -2a + 8 = 22

14a + 8 = 22

14a = 22 - 8

14a = 14

a =14/14

a = 1

replace the value of a in all the sides

the road will be

4(1) + 4(1) + 4(1) + 4(1) + 8 - 2(1) = 22 km

The roads are 4 km , 4 km, 4 km , 4 km and 6 km.