Question

the perimeter of a rectangular Garden is 72 m and area is 320 square metre find the length and the breadth of the garden. (from class 10 quadratic equation)​

Answer 1

Answer:

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Step-by-step explanation:

2l + 2b = 72m

⇒ l + b = 36m

⇒ b = 36m - l

Also,

lb = 320m²

l (36 - l) = 320

l² - 36l + 320 = 0

l² - 16l - 20l + 320 = 0

l ( l - 16) - 20 ( l - 16) = 0

( l - 16) ( l - 20 ) = 0

l = 16, 20

when l = 16m , b = 20m                                  when l = 20m , b = 16m

Answer 2

The length and the breadth of a rectangular garden are (20 m,16 m) or (16 m, 20 m).

GIVEN :

The perimeter of a rectangular garden = 72 m

Area of vegetable garden = 320 m²

To find :

The length and the breadth of the garden.

Formula used:

Area of rectangle = Length x breadth

Perimeter of rectangle = 2(Length + breadth)

Solution:

Let ‘x’ and ‘y’ be the length & breadth of the vegetable garden

Step 1: Make eq. by using the formula of Area of rectangle:

Area of rectangle = Length x breadth

xy = 320

$x = \frac{320}{y}$ …………….(1)

Step 2: Make quadratic eq. by using the formula of the perimeter of rectangle:

Given: Perimeter of a rectangular Garden = 72 m

$2(x + y) = 72$

$x + y = \frac{72}{2}$

$x + y = 36$

$\frac{320}{y} + y = 36$

[From eq. 1]

$\frac{(320 + y^{2} )}{y} = 36$

$320 + y^{2} = 36y$

y² - 36y + 320 = 0 ....... (2)

Step 3: Find breadth by middle term splitting method of prime factorization of eq. 2:

$\begin{array}{l}y^{2}-36 y+320=0 \\y^{2}-20 y-16 y+320=0 \\y(y-20)-16(y-20)=0 \\(y-16)(y-20)=0 \\y-16=0 \text { or } y-20=0\end{array}$

y = 16 or y = 20 ........(3)

Step 4: Find length by putting the values of y from eq. 3 in eq 1:

x = 320/y

If breadth, y = 16

$x = \frac{320}{16}$

x = 20 m

Length = 20 m

If  breadth,y = 20

$x = \frac{320}{20}$

x = 16 m

Length = 16 m

Hence, a rectangular garden’s length and breadth are (20 m,16 m) or (16 m, 20 m).

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