Question

80 points to answer this! Jasmine was helping her father mow the lawn. She knew that their front lawn was a square with an area of 64 m2. She liked to cut the grass by pushing the lawn mower in diagonal lines. To start, she pushed the lawnmower from one corner of the yard to the opposite corner. How long was the path she made to the nearest tenth of a metre?

Answer 1

Answer:

11.3m

Step-by-step explanation:

A=LW  It's a square, so the length and width would be the same.

8 X 8 is 64, so your sides would be 8m long

So the length of the sides would be 8m and drawing a line from corner to corner would make a 45 45 right triangle with sides 8m long.

in a 45 45 right triangle, you just have to multiply one leg by √2 to get the hypotenuse.  Therefore, to get the length of the lawn mower path from corner to corner, you would multiply 8 X √2 = 11.3m

Answer 2

We have

$A_{\square}=64\ m^2$

The formula of an area of a square:

$A_{\squre}=a^2$

Substitute:

$a^2=64\to a=\sqrt{64}\to a=8\ m$

Method 1:

Use the Pyhagorean theorem:

$a^2+a^2=d^2\\\\d^2=8^2+8^2\\\\d^2=64+64\\\\d^2=64\cdot2\to d=\sqrt{64\cdot2}=\sqrt{64}\cdot\sqrt2=8\sqrt2\ m\\\\\sqrt2\approx1.41\to8\sqrt2\approx8(1.41)=11.28\ m\approx11.3\ m$

Answer: 11.3 m

Method 2:

The formula of a diagonal of a square: $d=a\sqrt2$

Therefore we have $d=8\sqrt2\ m$

Answer: 11.3 m