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JAMB Mathematics 2023 Paper

Question : 74

Total: 80

Solution:

Concept:

The longer side of an isosceles right-angled triangle is the hypotenuse.

Use the perimeter and Pythagoras' theorem to find it.

Explanation:

Let each equal leg be

x

and the hypotenuse be

y

Perimeter

= 2

m, so:

y + 2x = 2

Hence:

y = 2 - 2x

Using Pythagoras' theorem:

y^2 = x^2 + x^2 = 2x^2

Thus:

y = x\sqrt{2}

Equate the two expressions for

y

2 - 2x = x\sqrt{2}

2 = x(2 + \sqrt{2})

x = \frac{2}{2 + \sqrt{2}} = 2 - \sqrt{2}

The longer side is the hypotenuse

y

y = 2 - 2x = 2 - 2(2 - \sqrt{2})

y = -2 + 2\sqrt{2}

Answer:

-2 + 2\sqrt{2}

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