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Question

Find the area and perimeter of an isosceles right-angled triangle, each of whose equal sides measures 10 cm. [Given: 2 = 1.41]

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Solution

Let:
Length of each of the equal sides of the isosceles right-angled triangle = a = 10 cm
And,
Base = Height = a
Area of isosceles right-angled triangle=12×Base×Height=12×10×10=50 cm2

The hypotenuse of an isosceles right-angled triangle can be obtained using Pythagoras' theorem.

If h denotes the hypotenuse, we have:

h2=a2+a2h=2a2h=2a h=102 cm

∴ Perimeter of ​the isosceles right-angled triangle = 2a+2a
=2×10+1.41×10=20+14.1=34.1 cm

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