Question

geometry
quiz (b): pythagorean theorem and trig
directions: show all work to receive full credit. place all final answers in the box provided.
use the pythagorean theorem to solve for x.
1.
2.

1. a walkway forms the diagonal of a square playground. the walkway is 30 meters long.

a) draw a picture representation.
b) find the side length of the square.
c) find the perimeter of the square.
$a^2 + b^2 = c^2$

Explanation:

Step1: Identify known sides, apply Pythagoras

For right triangle, $a^2 + b^2 = c^2$. Here $c=25$, $a=24$, solve for $x=b$.
$24^2 + x^2 = 25^2$
$576 + x^2 = 625$
$x^2 = 625 - 576 = 49$
$x = \sqrt{49} = 7$

Step2: Identify known sides, apply Pythagoras

Here $a=8$, $b=15$, solve for $x=c$.
$8^2 + 15^2 = x^2$
$64 + 225 = x^2$
$x^2 = 289$
$x = \sqrt{289} = 17$

Step3a: Draw square with diagonal

Draw a square, label each side $s$, label the diagonal (walkway) as 30 meters.

Step3b: Solve for square side length

Square diagonal: $s\sqrt{2} = d$. $d=30$, so:
$s = \frac{30}{\sqrt{2}} = \frac{30\sqrt{2}}{2} = 15\sqrt{2} \approx 21.21$ meters

Step3c: Calculate square perimeter

Perimeter $P=4s$.
$P = 4 \times 15\sqrt{2} = 60\sqrt{2} \approx 84.85$ meters

Answer:

1. $7$
2. $17$
3. a) (Square with side length $s$ and diagonal labeled 30 meters)

b) $15\sqrt{2}$ meters (or approximately 21.21 meters)
c) $60\sqrt{2}$ meters (or approximately 84.85 meters)