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

Answer:

The distance between library and museum is 400 yards.

Step-by-step 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,

$RM^2=LR^2+ML^2$

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

$\implies ML=\sqrt{RM^2-LR^2}$

By substituting the values,

$ML = \sqrt{500^2-300^2}$

$=\sqrt{250000-90000}$

$=\sqrt{160000}$

$=400$

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