Question

May u please help me with the 2 last Questions.

Answer 1

omeWe are asked to find the length of the diagonal of a square with side = 7 ft

So, we can use the Pythagoras Theorem to find its length, since we are dealing with a right anhle triangle that the diagonal determines, being the 7 ft sides the "legs" of the triangle, and the diagonal of the square being the hypotenuse:

`\text{hyp}=\sqrt[]{7^2+7^2}=\sqrt[]{49+49}=\sqrt[]{98}\approx9.899`

which can be rounded to about 9.9 feet for this diagonal.

In the second problem, we are given the value of the diagonal, and we are asked to find the value of the square's sides, so we use Pythagoras again:

`\begin{gathered} 12^2=x^2+x^2=2x^2 \\ 144=2x^2 \\ (144)/(2)=x^2 \\ 72=x^2 \end{gathered}`

where we have named "x" the length of the unknown sides of the square, and used that 12 is the length of the diagonal.

We solved for x^2, but now to find "x" (the length of the side) we use the square root property:

`\begin{gathered} x^2=72 \\ x=\sqrt[\square]{72} \\ x\approx8.485 \end{gathered}`

Then the sides of the square must be approximately 8.5 ft if we round the answer to one decimal.