Question

Gina 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 17 inches. The length of the diagonal of the floor of the room in the plan is approximately 18.79 inches.

Is the room in the shape of a square? Explain how you determined your answer. Show all your work.

Answer 1

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Let one wall is AB which length is 17 inches

and let diagonal of the floor of the room is AC which length is approximately 18.79 inche

so four walls of room are AB , BC , CD and DA

First Let ABCD is a square

$\angle \: D = 90 \degree \: \: \: \: ( \bold{given})$

In square ABCD

AD and DC are adjacent sides...and AC is diagonal of square

then..

AC² = AD² + DC²

since ABCD is a square so, AD = DC ( all sides of square are equal )

$\implies \: (18.79)^{2} = {17}^{2} + {17}^{2} \\ \\ \implies \: 353.06 = 289 + 289 \: \: \\ \\ \implies \: 353.06≠578 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so It contradicts that the diagonal of a square is equal to the root of square of it two sides..

so it is not a square

Answer 2

Given: Gina 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 17 inches. The length of the diagonal of the floor of the room in the plan is approximately 18.79 inches.

To find: Is the room in shape of a square?

Solution: Let the length of the four-walled room be a.

a= 17 inches

The diagonal of a square is equal to ✓2 times the length of any side.

Therefore, diagonal of the square

= ✓2 × length of side

= ✓2 a

= ✓2 × 17 inches

= 1.414 × 17 inches (✓2 = 1.414)

= 24.09 inches

But the length of the diagonal is given as 18.79 inches which is not equal to the calculated length of the diagonal of the square.

Therefore, the room is not in the shape of a square.