Question

the breadth of a rectangular Garden is 2/3 of its length. if its perimeter is 40m find its area

Answer 1

${\huge{\underbrace{\bf{\pink{Answer}}}}}$

Given:

⠀⠀ ⠀⠀

• The Breadth of are rectangular garden is (2/3) of the length value. And the perimeter is 40 cm.

⠀

⠀

To Find out :

⠀

• The area of the rectangular gardens =?

⠀

⠀

“Let suppose that the length of the Rectangular garden = x cm and then the value of the breadth B = (2/3)x cm.”

⠀

And we know that Perimeter P = 2(L+B)

☞2[x + (2/3)x]=40

☞(5/3)x = 20

☞x = (3×4)= 12 cm

⠀

So, the required value of the length x = 12 cm.

And the required value of the breadth B = (2/3)x= 8 cm

⠀

⠀

Hence area of garden = length × breadth

☞12 × 8

☞96 cm²

Answer 2

➤ Answer

• Area of the rectangular garden = 96m².

➤ Given

• The breadth of rectangular garden is ⅔ of it's length.

• Perimeter of rectangular garden = 40 m.

➤ To Find

• The area of rectangular garden.

➤ Step By Step Explanation

Given that the breadth of rectangular garden is ⅔ of it's length. Perimeter of rectangular garden = 40m.

So let's do it !!

➠ Assumption

Let us consider the length be x then breath will be ⅔ of x.

➠ By substituting the values.

Let's substitute the values in this formula ⤵

$\underline{\boxed{\bf{\green{Perimeter_{(Rectangle)} =2( Length + Breadth)}}}}$

$:\longmapsto\tt40 = 2 \bigg\{\cfrac{2x}{3} + x \bigg\} \\ \\:\longmapsto\tt 40 = 2\bigg\{\cfrac{2x + 3x}{3} \bigg\} \\ \\: \longmapsto\tt40 = 2\bigg\{\cfrac{5x}{3} \bigg\} \\ \\:\longmapsto\tt 40 = 2 \times \cfrac{5x}{3} \\ \\:\longmapsto\tt 40 = \cfrac{10x}{3} \\ \\:\longmapsto\tt 40 \times 3 = 10x \\ \\:\longmapsto\tt120=10x\\\\:\longmapsto\tt\cancel\cfrac{120}{10} = x \\ \\:\longmapsto\tt 12m = x$

Length = 12 m and Breadth = ⅔ × 12 => 8 m.

➠ By substituting the actual values

Now Area will be ⤵

$\underline {\boxed{ \bf{\pink{Area_{(Rectangle)} = Length \times Breadth}}}}$

$:\longmapsto\tt12 \times 8 {m}^{2} \\ \\:\longmapsto\tt Area = 96 {m}^{2}$

➵ Therefore, area of rectangular garden = 96 m².

__________________________