Question

The lengyh and perimeter of a rectangle are in the ratio 2:7 if perimeter of rectangle is 14 m find the area of the rectangle

Answer 1

Answer:

let length of the rectangle be 2x

breadth be 7x

perimeter of the rectangle=2(l+b)

14=2(2x+7x)

9x=14/2

x=7/9

length of the rectangle=2*7/9=14/9 m

breadth of the rectangle=7*7/9=49/9 m

Answer 2

Answer:

Area is 48 m²

Step-by-step explanation:

Since, the perimeter of a rectangle is,

$P=2(l + w)$

Where,

l = length,

w = width,

Here,

$\frac{l}{P}=\frac{2}{7}$

$\frac{l}{2(l+w)}=\frac{2}{7}$

$7l = 4(l+w)$

$7l = 4l + 4w$

$3l = 4w$

$l =\frac{4}{3}w-----(1)$

Now, according to the question,

$P = 14$

$\implies 2(l+w) = 14$

$l+w = 14$

From equation (1),

$\frac{4}{3}w + w = 14$

$\frac{4+3}{3}w= 14$

$7w = 42$

$\implies w = 6$

Again from (1), l = 4/3 × 6 = 4 × 2 = 8 m

Hence, the area of the rectangle,

$A = l\times w = 8\times 6 = 48\text{ square meters}$

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