Question

Perimeter of a rectangle is 70 cm.length is taken as x and area a(x). a) write relation between x and a(x)
b) find a(20) and a(15)
c) if a(7) = a(k).find the number k​

Answer 1

Answer:

Step-by-step explanation:

Perimeter of the rectangle=70cm

Length of the rectangle=xcm

We know,

Perimeter of the rectangle=2(length+breadth)

=>70=2(x+breadth)

=>

2

70

​

=x+breadth

=>x+breadth=35

=>breadth=35−x

Given,area of rectangular board=30cm

2

=>length+breadth=300

=>x(35−x)=300

=>−x

2

+35x−300=0

=>x

2

−35x+300=0

=>x

2

−20x−15x+300=0

=>x(x−20)−15(x−20)=0

=>(x−20)(x−15)=0

∴x−20=0 or x−15=0

=>x=20 or x=15

∴35−x=35−20 or ∴35−x=35−15  

    =15 or  =20

∴Dimensions are 15 and 20cm