Question
The sides of certain triangles are given below. Determine them are right triangles:
$7\ cm, 24\ cm, 25\ cm.$
$7\ cm, 24\ cm, 25\ cm.$
✓
Answer
For a given triangle to be a right angled, the sum of the squares of the two sides must be equal to the square of the largest side.
Let $a = 7\ cm, b = 24\ cm$ and $c = 25\ cm$, Then
$\big(\text{a}^2+\text{b}^2\big)=\big[7^2+(24)^2\big]\text{cm}^2$
$=(49+576)\text{cm}^2$
$=625\text{cm}^2$
$\text{c}^2=(25\text{cm})^2=625\text{cm}^2$
$\therefore\big(\text{a}^2+\text{b}^2\big)-\text{c}^2$
Hence, the given triangle is a right triangle.
Let $a = 7\ cm, b = 24\ cm$ and $c = 25\ cm$, Then
$\big(\text{a}^2+\text{b}^2\big)=\big[7^2+(24)^2\big]\text{cm}^2$
$=(49+576)\text{cm}^2$
$=625\text{cm}^2$
$\text{c}^2=(25\text{cm})^2=625\text{cm}^2$
$\therefore\big(\text{a}^2+\text{b}^2\big)-\text{c}^2$
Hence, the given triangle is a right triangle.
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