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# The Perimeter of an Isosceles Triangle is 42 Cm and Its BašE is (32) Times Each of the Equal Sides. Find the Length of Each Side of the Triangle, Area of the Triangle and the Height of the Triangle. - CBSE Class 9 - Mathematics

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ConceptArea of a Triangle by Heron’S Formula

#### Question

The perimeter of an isosceles triangle is 42 cm and its baše is (32) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.

#### Solution

Let ‘x’ be the measure of each equal sides

∴ Base =3/2x

∴x + x + 3/2x= 42       [∵ Perimeter = a + b + c = 42 cm]

⇒7/2x=42

⇒x= 12cm

∴Sides are a = x = 12 cm

b = x = 12 cm

c=x=3/2(12)cm = 18 cm

By heron’s formulae

∴ Area of triangle =sqrt(s(s-a)(s-b)(s-c)) cm^2

=sqrt(21(9)(9)(21-18)cm^2)

=sqrt((21)(9)(9)(3))cm^2

=71.42cm^2

∴ Area   of triangle = 71.42 cm^2

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#### APPEARS IN

Solution The Perimeter of an Isosceles Triangle is 42 Cm and Its BašE is (32) Times Each of the Equal Sides. Find the Length of Each Side of the Triangle, Area of the Triangle and the Height of the Triangle. Concept: Area of a Triangle by Heron’S Formula.
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