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in Perimeter and Area of Plane Figures by (30 points)
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The area of an isosceles right triangle is \( 392 cm ^{2} \). Find the hypotenuse.

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In an isosceles right angled triangle, the two sides on the right angle are equal.

Let the equal side be a

Hence, hypotenuse of the isosceles right angled triangle of side \(a = \sqrt{a^2 + a^2} = \sqrt2 a\)

In  the isosceles right triangle, the base and height = a

Hence, area of the triangle = \(\frac{1}{2} \times base \times height\)

\(\frac{1}{2} \times a \times a = 392 cm^2\) 

\(a^2 = 784\) 

a = 28 cm

And the hypotenuse = \(\sqrt2 a = 28 \sqrt2 cm\)

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