Question

Sides of triangles are given below. Determine which of them are right triangles? In case of a right triangle, write the length of its hypotenuse.

• A. $7\mathrm{cm},24\mathrm{cm},25\mathrm{cm}$
• B. $3\mathrm{cm},8\mathrm{cm},6\mathrm{cm}$
• C. $50\mathrm{cm},80\mathrm{cm},100\mathrm{cm}$
• D. $13\mathrm{cm},12\mathrm{cm},5\mathrm{cm}$

Answer 1

Answer: (A), (D)

$13\mathrm{cm},12\mathrm{cm},5\mathrm{cm}$

Explanation for the correct option:

Option (A): $7\mathrm{cm},24\mathrm{cm},25\mathrm{cm}$

Given:

$7cm,24\mathrm{cm},25\mathrm{cm}$

$\begin{array}{rcl}{\left(25\right)}^2& =& 25\times 25\\ & =& 625\end{array}$

Therefore, the are sides of a right triangle and hypotenuse $\mathbf{=}\mathbf{25}\mathbf{}\mathit{c}\mathit{m}$.

Option (D): $13\mathrm{cm},12\mathrm{cm},5\mathrm{cm}$

$13\mathrm{cm},12\mathrm{cm},5\mathrm{cm}$

$\begin{array}{rcl}{\left(13\right)}^2& =& 13\times 13\\ & =& 169\\ {\left(12\right)}^2+{\left(5\right)}^2& =& 169\end{array}$

Therefore, this is the sides of right triangle and hypotenuse $\mathbf{=}\mathbf{}\mathbf{13}\mathbf{}\mathit{c}\mathit{m}$.

Explanation for the incorrect options:

Option (B) $3\mathrm{cm},8\mathrm{cm},6\mathrm{cm}$

$3\mathrm{cm},8\mathrm{cm},6\mathrm{cm}$

$\begin{array}{rcl}{\left(8\right)}^2& =& 8\times 8\\ & =& 64\\ {\left(3\right)}^2+{\left(6\right)}^2& =& 45\end{array}$

So, not right triangle.

Option (C): $50\mathrm{cm},80\mathrm{cm},100\mathrm{cm}$

$50\mathrm{cm},80\mathrm{cm},100\mathrm{cm}$

$\begin{array}{rcl}{\left(100\right)}^2& =& 100\times 100\\ & =& 10000\\ {\left(50\right)}^2+{\left(80\right)}^2& =& 8900\end{array}$

So, not right triangle.

Therefore, option (B) and (C) are incorrect.