Question

A triangle and parallelogram have the same base and the same area if the side of the triangle are 34 CM 42 cm and 20 cm find the height of the parallelogram having 42 cm is equals to.​

Answer 1

Step-by-step explanation:

a=34

b=42

c=20

a+b+c

2

= 34 +42+20

2

= 96

2

= 48 answer

height find :_ 1

× base × height

2

= 1

× 42 × height

2

height = 21 answer

Answer 2

$\boxed{\tt{\bold{\red{\large{ANSWER}}}}}:-$

Given ,

☆ Sides of Triangle are 34cm , 42cm , 20cm

☆ Base of Parallelogram is 42cm

It is also given that ,

$\boxed{\purple{ \: Area \: of Parallelogram \: = Area \: of \: Triangle }} - - > 1$

$\boxed{\pink{Area \: of \: Parallelogram }}= Base × Height \:$

$\rightarrow{42 \times h}$

$\rightarrow{42h}$

$\boxed{\blue{Area \: of \: Triangle \: }} = \sqrt{s(s - a)(s - b)(s - c)}$

Here , s is the semi - perimeter ..

a , b , c are the sides of Triangle

Here ,

a = 34cm

b = 42cm

c = 20cm

So ,

$\boxed{\green{s = \frac{a + b + c}{2} }}$

$s = \frac{34 + 42 + 20}{2}$

$s = \frac{76 + 20}{2}$

$s = \frac{96}{2}$

$s = 48cm$

Now ,

$Area \: of \: Triangle = \sqrt{48(48 - 34)(48 - 42)(48 - 20)}$

$\rightarrow{ \sqrt{48(14)(6)(28)}}$

$\rightarrow{ \sqrt{112896} }$

$\rightarrow{336 {cm}^{2} }$

Now we will put the value of area of parallelogram and area of triangle in equation 1.

$\boxed{\purple{ \: Area \: of Parallelogram \: = Area \: of \: Triangle }}$

$\rightarrow{42 \times h = 336}$

$\rightarrow{h = \frac{336}{42} }$

$\rightarrow{h = 8 \: cm}$

$\bold{\large{\orange{Height \: of \: Parallelogram \: is \: 8 cm }}}$

$\bold{\large{\red{ I \: hope \: it \: helps \: u \: dear \: friend !! \: }}}$