Question

8. The sides of a rectangle are in the ratio 3 : 7 and its area is 1029 m². Find the dimensions of the rectangle, and then find its perimeter.

Answer 1

Step-by-step explanation:

length = 3x

breadth= 7x

area = 1029m2

area = length × breadth

(3x) × (7x)= 1029

$21 {x}^{2} = 1029 \\ \\ {x}^{2} = \frac{1029}{21} = 49 \\ \\ x^{2} = 49 \\ x = \sqrt{49} \\ x = \sqrt{7 \times 7} \\ x = 7$

now,

3×7=21

7×7=49

(verification 21×49=1029)

so length = 21

breadth = 49

now perimeter = 2(l+b)

=2(21+49)

=2(70)

= 140

so perimeter = 140m