Question

Answer the following
using two variables, write the following statements in
mathematical form:
i) The perimeter of a rectangle is 36cm.
ii). The ratio of two numbers is 3:8. iii)- Two years hence,
father's
age will be twiice the son's age then, iv)
number is
5 more than seven times the other number.
one​

Answer 1

Step-by-step explanation:

(I) Let length of rectangle be 'l'

Let breadth of rectangle be 'b'

So, perimeter of rectangle is = 2(l+b)

36 = 2(l+b)

36/2 = l+b

18 = l+ b

So required answer is l+b = 18

(ii) Let one number be 'x'

Let other number be 'y'

According to question :-

x/y = 3/8

8x = 3y

8x - 3y = 0

Required answer is 8x - 3y = 0

(iii) Let present age of son be 'x'

and present age of father be 'y'

Two year hence :-

Son's age become = x+2

Father's age become = y+2

According to question :-

y = 2x

2x - y = 0

Required answer is 2x - y = 0

(iv) Let greater number be 'x'

Let smaller number be 'y'

According to question :-

x = 7y + 5

x - 7y - 5 = 0

Required answer is x - 7y - 5 = 0

Answer 2

The correct answers are given below:

i) A rectangle has two variables, length, and breadth.

Let us assume that the length and breadth of the rectangle are 'l' and 'b' respectively.

We know that the perimeter of a rectangle = 2 x (length + breadth)

⇒The perimeter of the rectangle = 2 x (l + b)

Now we are given that its perimeter is 36cm.

⇒ 2l + 2b = 36 or l + b = 18.

∴ The correct answer is 2l + 2b = 36 or l + b = 18.

ii) Let us consider that the two numbers are 'x' and 'y'. We are given that the ratio of these two numbers is 3:8.

⇒ x:y = 3:8

⇒ 8x = 3y

⇒ 8x - 3y = 0

Hence the correct answer is x:y = 3:8 or 8x - 3y = 0.

iii) Let us assume that the father's and son's present ages are 'x' and 'y' respectively.

Two years from now,

The father's age = (x+2) years

The son's age = (y+2) years

We are given that two years hence, the father will be twice the son's age then. In statement form, we have

(x+2) = 2(y+2)

⇒ x-2y = 2

Hence the correct answer is (x+2) = 2(y+2) or x-2y = 2.

iv) Let us assume that the two unknown numbers are 'p' and 'q' respectively, where 'p' is the greater of the two.

We are given that one number is 5 more than seven times the other number.

i.e. p = 7q+5

⇒ p-7q = 5.

Hence the correct answer is p = 7q+5 or p-7q = 5.

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