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.

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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.

Check:7² + 24² = ? 25²7² = 4924² = 57625² = 625

Now calculate:49 + 576 = 625

✅ 49 + 576 = 625, so:7² + 24² = 25²This confirms the triangle is a right triangle.

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What Type of Right Triangle is It?

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.

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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

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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

With sides 7, 24, and 25 meters, this triangular land offers a clean, measurable shape — and a generous area of 84 m², easily usable for small garden plots, outbuildings, or divided sections.

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Summary

• The triangle with sides 7 m, 24 m, and 25 m is a right triangle.- Confirmed via the Pythagorean Theorem: 7² + 24² = 25²- Area = \(\frac{1}{2} \ imes 7 \ imes 24 = 84 \ ext{ m²}\)- A smart, geometric solution for anyone assessing triangular plots

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If your next project involves land or construction, verifying triangle types before calculations can save time and ensure precision. A right triangle like this one isn’t just mathematically perfect—它’s practical too!

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Keywords: triangular plot area, right triangle 7-24-25, area of right triangle, check if triangle is right, land shape calculation, geometry for landowners