Question

if the area of rectangle is 24 metre square and it's perimeter is 20 m the equation to find it's length and breadth would be​

Answer 1

Answer:

the answer is here....

Answer 2

The equation to find its length and breadth would be y² - 10 y + 24 = 0, .

The length and breadth of a rectangle are (6 m, 4 m) or (4 m, 6 m).

GIVEN :

The perimeter of the rectangle = 20 m

Area of rectangle = 24 m²

To find:

The equation to find its length and breadth.

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 rectangle.

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

Area of rectangle = Length x breadth

xy = 24

$x = \frac{24}{y}$…………….(1)

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

Given: Perimeter of a rectangular Garden = 72 m

$\begin{array}{l}2(x+y)=20 \\\left(\frac{24}{y}+y\right)=\frac{20}{2}\end{array}$

[From eq.1]

$\begin{array}{l}\left(\frac{24}{y}+y\right)=10 \\\frac{\left(24+y^{2}\right)}{y}=10 \\24+y^{2}=10 y \\y^{2}-10 y+24=0\end{array}$………(2)

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

$y^{2}-10 y+24=0$

$\begin{array}{l}y^{2}-6 y-4 y+24=0 \\ y(y-6)-4(y-6) =0 \\ (y-4)(y-6)=0 \\y - 4 = 0 \text { or } y - 6=0 \\y= 4 \text { or } y=6\end{array}$

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

$x = \frac{24}{y}$

If breadth, y = 4

$x = \frac{24}{4}$

x = 6 m

Length = 6 m

If breadth, y = 6

$x = \frac{24}{6}$

x = 4 m

Length = 4 m

Hence, the equation to find its length and breadth is y² - 10 y + 24 = 0, and a length and breadth of a rectangle are (6 m,4 m) or (4 m, 6 m).

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