Question

the perimeter of an isosceles triangle is 42 cm and its base is one and a half times each of its equal sides. Find the area of the triangle
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Answer 1

Answer:

perimeter of an isosceles triangle =

2a ( isosceles triangle has two equal sides ) + b ( base )

here, b = 1.5 a ( 3/2 a )

here, perimeter = 42 cm

42 = 2a + 1.5 a

42 = 3.5 a

a = 42/3.5

a = 12

Therefore,

the two equal sides = 12 cm

base = 3/2 * 12 = 18 cm

Verification:

12 + 12 + 18 = 42 cm

Answer 2

Answer:

Step-by-step explanation:

Given

perimeter= 42cm

Let the equal sides of isosceles triangle be x

then, base = 1.5x

Now,

Perimeter of Triangle= sum of all sides

1.5x+x+x=42

3.5x=42

x=42/3.5

x=12

Perimeter=42

semiperimeter = 42/2=21 = s

Using herons formula

$\sqrt{s(s-a)(s-b)(s-c)}$

$\sqrt{21(21-12)(21-12)(21-18)}$

$\sqrt{21(9)(9)(3)}$

$\sqrt{7*3*3*3*3 }$

9$\sqrt{7}$cm^2^