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Question
Find the area and perimeter of an isosceles right angled triangle, each of whose equal sides measure 10cm.
Solution
Let:
Length of each of the equal sides of the isosceles right-angled triangle = a = 10 cm
And.
Area of isosceles right – angled triangle=`1/2xxBasexxHeight`
The hypotenuse of an isosceles right – angled triangle can be obtained using Pythagoras’ theorem
If h denotes the hypotenuse, we have:
`h^2=a^2+a^2`
⇒`h=2a^2`
⇒`h=sqrt2a`
⇒`h=10sqrt2 cm``
∴ Perimeter of the isosceles right-angled triangle = `2a+sqrt2a`
=`2xx10+1.41xx10`
=`20+14.1`
=`34.1 cm`
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