Question

find its height.
The base and height of a parallelogram are in the ratio 3 : 2 and its area is 600 m then find the base and height of the parallelogram ​

Answer 1

Solution :

Let base of parallelogram be 3x and height be 2x

$\star \sf \: Given \: Area = 600 {m}^{2}$

$\bold{\large{\boxed{\sf{\purple{Area \: of \: parallelogram \: = Base \: \times Height}}}}}$

$\hookrightarrow \sf \: 600 = 3x \times 2x$

$\hookrightarrow \sf \: 600 = 6 {x}^{2}$

$\hookrightarrow \sf \: {x}^{2} = \cancel\dfrac{600}{6}$

$\hookrightarrow \sf \: {x}^{2} =100$

$\hookrightarrow \sf \: x = \sqrt{100}$

$\sf \: x = \large \boxed{ \sf \: \red{10 \: m}}$

$\star \sf \: Height \: = 2x = 2 \times 10 = \boxed{ \green{ \sf \: 20 \: m}}$

$\star \sf \: Base \: = 3x = 3 \times 10 = \boxed{ \blue{ \sf \: 30 \: m}}$

Verification :

$\star \: \bold \red{Area = base \: \times \: height}$

$\hookrightarrow \sf \: 600 = 20 \times 30$

$\hookrightarrow \sf \: 600 = 600$

Hence, Verified!

More About Parallelogram :

$\star$ A quadrilateral in which both the pair of opposite sides are parallel is called as Parallelogram.

$\star$ Opposite angles of parallelogram are equal.

$\star$ Opposite sides of Parallelogram are equal.

$\star$ Diagonals of parallelogram bisect each other.

Answer 2

Answer:

Base = 30 m and Height = 20 m

Step-by-step explanation:

Let the unit constant be k.

We have :

Base = 3 k

Height = 2 k

We know :

Area of parallelogram = Base × Height.

We have given Area of parallelogram = 600 m²

600 = 3 k × 2 k

k² = 600 / 6

k² = 100

k = ± 10 .

We know side cannot be negative.

Hence , base = 30 m and height = 20 m .