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? - liviu.dev
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:
The Secret Hide Behind Unsinkable, Soundproof Your Home Why Every Home Needs the Aesthetic Heavyweight of Rubber Flooring Can This Hidden Floor Solution End Your Floor Pain For Good?Final 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