Question

An isosceles right-angled triangle has an area of 900 cm². What is the length of the hypotenuse?

Answer 1

Dear Student.

$$\begin{gathered} Since,thisisanisoscelestriangle,height=base. \\ Sinceareaoftriangle=\frac{1}{2}\times base\times height \\ Thereforeequatingitwiththegivenarea: \\ \frac{1}{2}\times bas{e}^2=900 \\ base=\sqrt{900\times 2}=30\sqrt{2}cm \\ height=30\sqrt{2}cm \\ ByPythagorasTheorem: \\ Hypotenuse=\sqrt{bas{e}^2+heigh{t}^2} \\ =\sqrt{{\left(30\sqrt{2}\right)}^2+{\left(30\sqrt{2}\right)}^2}=\sqrt{1800+1800} \\ =\sqrt{3600}=60cm \\ Thereforethelengthofhypotenuseis60cm \end{gathered}$$

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