Question**: A triangular plot of land has sides measuring 7 meters, 24 meters, and 25 meters. Is the triangle a right triangle, and if so, what is its area? - IQnection
Is a Triangle with Sides 7 m, 24 m, and 25 m a Right Triangle? Calculate Its Area
Is a Triangle with Sides 7 m, 24 m, and 25 m a Right Triangle? Calculate Its Area
If you’ve come across a triangular plot of land with side lengths 7 meters, 24 meters, and 25 meters and wondered whether it forms a right triangle, you’re in the right place. Not only can we determine this with a simple math test, but we’ll also calculate the area of this promising plot of land.
Understanding the Context
How to Check if a Triangle is a Right Triangle
A triangle is a right triangle if the sides satisfy the Pythagorean Theorem:
a² + b² = c², where c is the longest side (hypotenuse).
Given sides:
- 7 m
- 24 m
- 25 m
First, identify the largest side:
25 m is the longest side → likely the hypotenuse.
Image Gallery
Key Insights
Check:
7² + 24² = ? 25²
7² = 49
24² = 576
25² = 625
Now calculate:
49 + 576 = 625
✅ 49 + 576 = 625, so:
7² + 24² = 25²
This confirms the triangle is a right triangle.
What Type of Right Triangle is It?
🔗 Related Articles You Might Like:
📰 s2 express grill 📰 twisted flamingo sonic 📰 oegadgib 📰 Watch Your Bubble Game Shatterunbelievable Bubble Shooter Action Thatll Blow Your Mind 3065816 📰 Intrinsic Motivation 5502131 📰 Unleash Korean Pop Magic With Ondemandkorean Does It Really Have Everything You Need 8560193 📰 The Guy Next Door Subtly Changed My Whole Worldwatch What He Did Next 1789395 📰 X Men Evolution The Hidden Plot Twists That Will Make You Rewatch Every Scene 9642840 📰 Cwl Jonesboro Ar The Hidden Secrets Revealed Youre Not Supposed To See 6110556 📰 Experts Warn Nmrk Stock Is Poised To Explodeheres Why You Should Act Fast 5803470 📰 Kendra Scott Love Shack Fancy 4292466 📰 How Many Yards Is A Football Field The Reveal That Will Change Your Game 4496696 📰 When Amataur Spins Out Of Control Relentless Beast Moves Freak Out 5336294 📰 Best High Yield Etf Ever Shop Now Before It Elevates Your Portfolio Like Never Before 2081849 📰 Cinepolis Davenport 9294356 📰 Roblox Legacyverse 8240217 📰 American Funds Europacific Gr R6 9441225 📰 Red Violet Uncovered Why This Color Blend Behind The Trends 5195600Final Thoughts
This triangle has sides that are a multiple of the classic 3-4-5 triangle scaled by 7:
- 7 → 3×7 = 21? No — wait, actually 7-24-25 is a well-known Pythagorean triple.
Indeed, 7² + 24² = 25² proves it’s a valid right triangle, though not one of the smallest well-known ones.
How to Calculate the Area of the Triangle
For a right triangle, the area is simply:
\[
\ ext{Area} = \frac{1}{2} \ imes \ ext{base} \ imes \ ext{height}
\]
Using 7 m and 24 m as the legs (since they’re perpendicular):
\[
\ ext{Area} = \frac{1}{2} \ imes 7 \ imes 24 = \frac{1}{2} \ imes 168 = 84 \ ext{ m²}
\]
✅ Area = 84 square meters
Why This Matters for Landowners
Knowing whether a plot is a right triangle helps in:
- Calculating exact land area
- Planning structures or fencing
- Optimizing space usage in construction or landscaping
