Fiona’s school has three hallways that make up three sides of a triangular building design. in the morning, fiona walks 90 yards through the first hallway to get to the next. in the afternoon, she walks 60 yards through a second hallway to exit the building. what are the possible lengths of the third hallway that she did not walk through?

Solution:

It is given Fiona’s school has three hallways that make up three sides of a triangular building design .The two sides of the triangle are given as 90 yards and 60 yards. We need to find the possible lengths of the third hallway that she did not walk through.

Let the third side measure x yards.

By triangle inequality Theorem we have:The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

x+60>90                                       90+60> x

x> 30.                                            150>x or x<150.

The third side should be greater than 30 yards and less than 150 yards.

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.