Question

Riya has a field with a flowerbed and grass land. The grass land is in the shape of rectangle while flowerbed is in the shape of square. The length of the grassland is found to be 3 m more than twice the length of the flowerbed. Total area of the whole land is 1260 m2.
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(a) If the length of the flowerbed is x m then what is the total length of the field?
(1) (2x + 3) m (2) (3x + 3) m (3) 6x m
(b) What will be the perimeter of the whole field?
(1) (8x + 6) m (2) (6x + 8) m (3) (4x + 3) m
(c) What is the value of x if the area of total field is 1260 m2?
(1) 21 m (11) 10 m​

Answer 1

given the area of total land and relation between lengths of a rectangular grassland and square flowerbed, answer the flowing questions

Explanation:

1. let the side length of the square flower bed be 'x', length of rectangular grassland be 'l' and width of rectangular grass land be 'b'. then we have,    $l=(2x+3)m\ \ \ \ \ \ b=(x)\ m$                                                                             (-> referring to the figure given in the attachment)
2. now let the length of the whole field be 'L' and width of the whole field be 'B' then perimeter 'P' and area 'A' of the whole land is,                            $L=l+x=(3x+3)m \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ->ANS(a)\\B=b=(x)m\\P=2(L+B)=(8x+6)m\ \ \ \ \ \ \ \ \ \ \ ->ANS(b)\\A=L(B)=(3x^2+3x)m^2$    ----(i)
3. now given that $A=1260\ m^2$ we have,                                                                          $3x^2+3x=1260\\x^2+x-420=0\\(x+21)(x-20)=0\\x=-21\ or\ 20$        
4. since length cannot be negative we get  $x=20m$ [ANS(c)]        

Answer 2

Answer:

a) (2) 3x+3 m

b) (1) 8x+6 m

c) (3) 20 m

d) (4) 860m

e) (1) 20/43

Step-by-step explanation:

a) Let the length be xm , then the length of the field = x+ (3+2x)

                                                                                       = 3x+3 m

b) Perimeter of flowerbed + Perimeter of grassland= Perimeter of whole field = 2 (l+b) = 2(3x+3 + x)

                       = 2(4x+3)

                        = 8x+6 m

c) Area of field= Area of grassland + Area of flowerbed = lb + s²

                                                                                    1260= (3+2x)(x) + x²

                                                                                     1260= 3x+2x² +x²

                                                                                       3x² +3x-1260= 0

                                                                                       x² +x-420= 0

                                                                                        x² +21x- 20x-420= 0

                                                                                         x= 20, x= -21

                                       Length cannot be negative, ∴ x=20m

d) lb= 3+2x(x)= 3+ 2(20) (20) = 3+ 40 (20) = 43 *20 = 860m²

e) Area of flowerbed  =  (20)²  = 400 =  20    

   Area of grassland       860        860     43