Question

The perimeter of an isosceles triangle is 32 cm. If the ratio of the equal side to its base is 3 : 2, then the area of triangle is 

32√2

32

16

16√2

​

Answer 1

given:

perimeter = 32cm

ratio of sides is 3:2

to find:

the area of the triangle

solution:

since the ratio is given as 3:2,

we'll take the ratio constant to be 'x'

thus, the sides become :

equal sides = 3x

base = 2x

----------------------------------------------------

perimeter given is 32cm

we know that,

$\boxed{\red{\tt perimeter=sum\:of\:all\:sides}}$

using this formula,

$\tt 32 = 3x +2x+3x$

$\tt 32=8x$

$\tt \cancel\dfrac{32}{8}=x$

$\tt 4=x$

the sides become :

equal sides = 3x = 12cm

base = 2x = 8cm

______________________________

the area of equilateral triangle can be given by the herons formula

semi perimeter = perimeter / 2 = 16cm

s-a = 16-12=4 cm

s-b = 16-8=8cm

s-c=16-12=4 cm

area = root[ (16)(4)(4)(8)]

area = root [4×4×4×4×4×2]

area = 4×4×2root (2)

area = 32root2

hence, option a will be correct.

calculating area,

here for calculating the area of isosceles triangle It is better to use the herons formula as it is less time consuming and easy to solve in.

The things you need for herons formula Is the semi perimeter ..which is half of the perimeter.

then you place the values in the herons formula.

isosceles.

when two sides of a triangle are equal on magnitude,they are recognizer as isosceles triangles.

hope this helps you out........

Answer 2

Answer:

32√2

Step-by-step explanation:

please check the attachment