Question

The side of a triangle are 39cm, 42cm and 45cm. A parallelogram stands on the greatest side of the triangle and has the same area as that of the triangle. Find the height of the parallelogram.

Answer 1

Answer:

16.8 cm

Step-by-step explanation:

We are given that  a triangle with sides 39 cm ,42 cm and 45 cm.

A parallelogram stands on the greatest side =Base of parallelogram=45 cm

Semi perimeter of triangle =s=$\frac{a+b+c}{2}=\frac{39+42+45}{2}=63 cm$

Area of triangle by herone's fomrula

Area of triangle =$\sqrt{s(s-a)(s-b)(s-c)}$

Substitute the values

Area of triangle =$\sqrt{63\cdot24\cdot21\cdot 18}$

=$756 cm^2$

Area of parallelogram=Area of triangle =$756 cm^2$

Area of parallelogram=$base\times height$

$756=45\times height$

$height=\frac{756}{45}=16.8 cm$

Answer 2

Answer:

We are given that a triangle with sides 39 cm ,42 cm and 45 cm.

A parallelogram stands on the greatest side =Base of parallelogram=45 cm

Semi perimeter of triangle =s=\frac{a+b+c}{2}=\frac{39+42+45}{2}=63 cm

2

a+b+c

=

2

39+42+45

=63cm

Area of triangle by herone's fomrula

Area of triangle =\sqrt{s(s-a)(s-b)(s-c)}

s(s−a)(s−b)(s−c)

Substitute the values

Area of triangle =\sqrt{63\cdot24\cdot21\cdot 18}

63⋅24⋅21⋅18

=756 cm^2756cm

2

Area of parallelogram=Area of triangle =756 cm^2756cm

2

Area of parallelogram=base\times heightbase×height

756=45\times height756=45×height

height=\frac{756}{45}=16.8 cmheight=

45

756

=16.8cm