# 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. - Mathematics

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

Concept: Area of a Triangle by Heron's Formula
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.1 | Q 10 | Page 8

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