Question

Geometry- Please help!

Answer 1

Kim designs a walkway along the diagonal of the rectangular lawn shown below.

Answer 2

Which statement is true about the length of the walkway?

Answer 3

???

Answer 4

oh sorry lol

Answer 5

It is less than 10 meters because 2(19 – 15) = 8
It is equal to 16 meters because (19 - 15)2 = 16
It is between 10 and 15 meters because √19^2-15^2 = 11.6
It is between 20 and 25 meters because √ 15^2+19^2 = 24.2

Answer 6

We have a right triangle here (well, 2 actually, but let's just consider one). In all right triangles, the hypotenuse will be longer than the 2 other sides. Just think of Pytagoras, c^2 = a^2+b^2, and it becomes clear that c > a or b (but never greater than a+b)

Answer 7

So would it be "It is between 20 and 25 meters because √ 15^2+19^2 = 24.2" ?

Answer 8

exactly, because that's the only answer that's bigger than 19. And that also happens to be mathematically correct, but point is, you don't even have to press a single button on your calculator to answer it, because you now know that your answer needs to be bigger than 19 :-)

Answer 9

Thanks! That will save me some time lol