Question

Your teacher just moved into a new house with a yard! The house is beautiful, but the back yard needs some TLC.
They've been inspired by a
makeover show and want to have a garden hangout in one of the corners to make the backyard feel more inviting.
Can you help make their wish come true?
Your teacher wants to have a garden space in one of the corners to make their backyard feel more inviting!
The space should be triangular and large enough to fit at least 3 flower planters.

The first chunk of your project is to:
• Identify the corner of the yard to be remodeled, and determine reasonable lengths for the 3 sides of the garden/patio space (slide 4-
• Find the hypotenuse measure for your triangular space using the pythagorean theorem. (slide 4)
• Calculate the area of the space (slide 4)
Building Block 1
Example
a2 + b2 - c2 (5)2 + (3.5)2= c2
Area
(base) (height)
A=(3.5ft)(5ft)
25+12.25
c2
37.25
A 8.75 ft2
√37.25 c
5
6.10 ft
6.103
c
3.5 ft
Note:
If your hypotenuse is a decimal, write the value to the thousandths place (6.103) then round the length to hundredths (6.10).

Scoring Total for the Duding
Using the Pythagorean Theorematic
Makers of prob
P
Draw your right triangle to represent your deck in this bioprint as big or small as you would like using the straight line tool
20 feet
34 feet
What are the lengths of the side of your patio? "Include units of measurelederent
Lega= Logb
"Use the pythagorean theorem to find the length of side c (hypotenuse). Show all calculations/work below.
Side c (hypotenuse)
What is the area of your deck? Show all calculations/work below.
✔Fosfora
PSSA Reece Shoot
Demos Calculator
Reflection. Your answers must be written in full sentences:
Are your side lengths reasonable for creating a garden space to fit at least 3 planters? Why do you think this?
What do you notice about the hypotenuse of the proposed triangular space compared to the legs?
"the down and function
In Crick is not working
your work in

Answer 1

Corner chosen:
- Back-left corner of the yard. I will place the triangular garden with its two legs along the two fences that meet at that corner.

Side lengths (including units):
- Leg a (along one fence) = 8 ft
- Leg b (along the other fence) = 6 ft
- Hypotenuse c (across the yard) = ? ft

Use the Pythagorean Theorem to find the hypotenuse:
- a^2 + b^2 = c^2
- (8 ft)^2 + (6 ft)^2 = c^2
- 64 ft^2 + 36 ft^2 = c^2
- 100 ft^2 = c^2
- c = √100 ft^2 = 10 ft

So side c (hypotenuse) = 10 ft.

Area calculation:
- Area of a right triangle = (1/2) × base × height
- A = (1/2) × 8 ft × 6 ft
- A = (1/2) × 48 ft^2 = 24 ft^2

Reflection (full sentences):
1. Are the side lengths reasonable for creating a garden space to fit at least 3 planters? Why do you think this?
- Yes. A 24 ft^2 triangular area is large enough to fit at least three planters comfortably. For example, three medium planters each with a footprint around 1.5–2 ft^2 would use about 4.5–6 ft^2 total; the remaining area allows for spacing between planters and a small path to tend them.

2. What do you notice about the hypotenuse of the proposed triangular space compared to the legs?
- I notice that the hypotenuse (10 ft) is longer than either leg (8 ft and 6 ft). It also equals the square root of the sum of the squares of the legs (√(8^2 + 6^2) = 10), which is the relationship required by the Pythagorean Theorem.

If you’d like, I can show an alternate triangle size (longer or wider), sketch a simple layout for placing the three planters, or convert these measurements to meters.