Question

The roads that connect three buildings form a right triangle. Use the image to find the distance between the library and the museum.

Answer 1

knowing a² + b² = c²

a = 300 yards
b = ?
c = 500 yards

so plugging into the equation gives 300² + b² = 500², solving for b
b² = 500² - 300²
b = √(160000 = 400 yards

Answer 2

The distance between library and museum is 400 yards.

Explanation:

Let L represents the position of library, R represents the restaurant and M represents the museum,

Since, By the given diagram,

∠MLR = 90°,

LR = 300 yd,

RM = 500 yd,

So, by the Pythagoras theorem,

`RM^2=LR^2+ML^2`

`\implies ML^2=RM^2-LR^2`

`\implies ML=√(RM^2-LR^2)`

By substituting the values,

`ML = √(500^2-300^2)`

`=√(250000-90000)`

`=√(160000)`

`=400`

Hence, the distance between library and museum is 400 yards.