Right Triangles Unit | Mrs. E Teaches Math - Free Printable

Let’s solve this step by step.

We are given a right triangle garden with:
- One leg = 88 inches
- Hypotenuse = 137 inches
- Other leg = x inches (unknown)

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Step 1: Find the missing side (x) using the Pythagorean Theorem

In a right triangle:
a² + b² = c²
where c is the hypotenuse.

So:
88² + x² = 137²

Calculate squares:
88² = 7744
137² = 18769

So:
7744 + x² = 18769
→ x² = 18769 - 7744 = 11025
→ x = √11025 = 105

✔ So, the third side is 105 inches.

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Question 1: Find the perimeter of the garden.

Perimeter = sum of all sides = 88 + 105 + 137

Add them:
88 + 105 = 193
193 + 137 = 330

✔ Perimeter = 330 inches

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Question 2: Plant a post every 15 inches around the perimeter. How many posts?

Total perimeter = 330 inches
Posts every 15 inches → divide 330 ÷ 15 = 22

But wait — when you go around a closed shape (like a triangle), if you place a post at the start and then every 15 inches, the last post will be at the same spot as the first one. So we don’t double-count.

Example: Imagine a square with perimeter 60 inches, posts every 15 inches → 60 ÷ 15 = 4 posts. That works because each corner gets one post, and they’re spaced evenly.

Same here: 330 ÷ 15 = 22 → exactly 22 posts needed, since it divides evenly and the last post lands on the starting point.

✔ Number of posts = 22

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Question 3: Cost to enclose the garden

Costs:
- Each post costs $1.25
- Fencing costs $0.70 per foot

First, find cost of posts:
22 posts × $1.25 = ?

22 × 1.25 = 22 × (5/4) = (22 × 5)/4 = 110/4 = $27.50

Now, fencing:
Fencing goes along the entire perimeter → 330 inches

But fencing cost is per foot, so convert inches to feet:

330 inches ÷ 12 = 27.5 feet

Cost of fencing: 27.5 ft × $0.70 = ?

27.5 × 0.70 = (27 × 0.70) + (0.5 × 0.70) = 18.90 + 0.35 = $19.25

Total cost = posts + fencing = $27.50 + $19.25 = $46.75

✔ Total cost = $46.75

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Final Answer:
1) 330 inches
2) 22 posts
3) $46.75