Question

The base of a parallelogram is thrice its height. If the area is 897 sq.cm. Find the base and the height of parallelogram.

Answer 1

Answer:

$\boxed{ \bold{ { \sf{height \: = \: 17.29 \: cm}}}}$

$\boxed{ \bold{ \sf{base = 51.87 \: cm}}}$

Step-by-step explanation:

Let the height of a parallelogram be 'x'

Base of a parallelogram be 3x

Area of a parallelogram ( A ) = 897 cm²

Base ( b ) = ?

Height ( h ) = ?

First, finding the height of a parallelogram ( x )

$\bold{ \boxed{ \sf{area \: of \: a \: parallelogram \: = \: base \: \times \: height}}}$

$\dashrightarrow{ \sf897 = 3x \times x}$

$\dashrightarrow{ \sf{897 = 3 {x}^{2} }}$

$\dashrightarrow{ \sf{3 {x}^{2} = 897}}$

$\dashrightarrow { \sf{ \frac{3 {x}^{2} }{3} = \frac{897}{3} }}$

$\dashrightarrow{ \sf{ {x}^{2} = 299}}$

$\dashrightarrow{ \sf{x = \sqrt{299} }}$

$\dashrightarrow{ \sf{x = 17.29}}$

Height of a parallelogram = 17.29 cm

Finding the base of the parallelogram

$\sf{base \: of \ \: a \: parallelogram = 3x}$

⇒$\sf{base \: of \: a \: parallelogram = \: 3 \times 17.29}$

⇒$\sf{base \: of \: a \: parallelogram = 51.87 \: cm}$

Base of a parallelogram = 51.87 cm

Hope I helped!

Best regards! :D