Matt 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 19 inches. the length of the diagonal of the floor of the room in the plan is approximately 20.62 inches. is the room in the shape of a square? explain how you determined your answer. show all your work. asap

No, the room is not in the shape of a square

Step-by-step explanation:

First I multiplied 19 by 4 to get the perimeter if it was a square. Then I divided that by 2 to get 38 or the perimeter of half of the room if it is a square. Half of a square could be a triangle depending on how you cut it in half. And the given information tells me that all the walls meet at a 90-degree angle which means that the triangle is a right triangle. Since it's a right triangle I can use the Pythagorean theory to figure out the distance that the long side of the triangle is which is the same as the diagonal of the floor plan if it is a square. So I do 19^2+19^2=26.87^2. Therefore, the room is not the shape of a square since the answer isn't the same as the diagonal.

the answer is 45 i just did it on oddesy ware

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4