Question

The area of a square courtyard is equal to the area of a rectangular courtyard
whose length is eight meters more than the side of the square courtyard and
whose width is six meters more than the side of the square court yard. Find the
dimensions of the square and rectangular courtyards.

Answer 1

Correct option is

B

21 cm

Breadth of a rectangular courtyard =3.78m=378cm

Length of a rectangular courtyard =5.25m=525cm

Now, we have to find H.C.F os 378 and 525

378=2×3×3×3×7

525=5×5×3×7

Common factore=3×7

∴ H.C.F=21

Hence largest size of square tiles that can be paved exactly with square tiles is 21cm.

Answer 2

Answer:

Here is your answer.↓↓

Step-by-step explanation:

Here,

area of the square courtyard=area of the rectangular courtyard

=>(side×side)sq units=(length×width)sq units

Let the length of the side of the square courtyard be x m.

Then, (x×x)m²={(x+8)×(x+6)}m²

=>x²=(x+8)(x+6)

=>x²=x²+6x+8x+48

=>x²–x²–6x–8x=48

=>–14x=48

=>x=48/–14

=>x=–3.42

Hence, side of the square courtyard=3.42m

[Since, –3.42×(–3.42)=11.6964; which is positive. So, it can be written as 3.42m.]

and length of the rectangular courtyard

=(–3.42+8)m

=4.58m

and its width

=(–3.42+6)m

=2.58m.

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