Question

Find the area of an isosceles triangle whose base is 6 cm and perimeter is 16 cm

Answer 1

Answer:

12cm^2

Step-by-step explanation:

In an isosceles triangle 2 sides are equal

So, perimeter of triangle = a+b+c

                             16 = 6+6+x

                            16  =12+x

                             16-12=4

area =1/2*b*h

1/2*6*4

12cm^2

Answer 2

It is given that

Base = 6 cm

Perimeter = 16 cm

Consider ABC as an isosceles triangle in which

AB = AC = x

So BC = 6 cm

We know that

Perimeter of △ABC = AB + BC + AC

Substituting the values

16 = x + 6 + x

By further calculation

16 = 2x + 6

16 – 6 = 2x

10 = 2x

So we get

x = 10/2 = 5

Here AB = AC = 5 cm

BC = ½ × 6 = 3 cm

In △ABD

AB2 = AD2 + BD2

Substituting the values

52 = AD2 + 32

25 = AD2 + 9

By further calculation

AD2 = 25 – 9 = 16

So we get

AD = 4 cm

Here

Area of △ABC = ½ × base × height

Substituting the values

= ½ × 6 × 4

= 3 × 4

= 12 cm2

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