Maria looks at the architectural plan of a four-walled room in which the walls meet each other at right angles. The length of one wall in the plan is 13 inches. The length of the diagonal of the floor of the room in the plan is approximately 15.26 inches. Is the room in the shape of a square? Explain how you determined your answer. Show all your work.

The length of one wall in the room plan is 13 in. If the room was square, all the sides would need to be 13 in.

Since the walls are at right angles, we can use the Pythagorean Theorem to solve this. (a^2 + b^2 = c^2)

(I drew a diagram. It looks like this: A square is cut across diagonally by a line labeled "hypotenuse, 15.26 in." The right triangle created by the line is lightly highlighted. The sides of the triangle adjacent to the right angle are labeled "leg a, 13 in." and "leg b, ?" for unknown value. Picture is attached!)

To find the value of the unknown leg, we can subtract the value of leg a from the hypotenuse to find the value of leg b.

c^2 - a^2 = b^2

Insert values into equation and solve.

15.26^2 - 13^2 = b^2

232.87 - 169 = b^2

Square root of 63.87 = b

The value of the unknown leg would be 8 inches. Since all sides of the room would have to be 13 inches for the room to be square, the room is a rectangle.

c. 65°

step-by-step explanation:

we are given a triangle with two known angles, 62° and 53°, while the third angle x is unknown and we are to find its value.

we know that the sum of angles in a triangle is equal to a total of 180 degrees. so we can write it as:

x + 62° + 53° = 180°

solving to find the value of x:

x = 180 - (62 + 53) = 65°

therefore, the value of x in this triangle is 65°.

y > 1/3x

y < = -x + 4

hope this : )