Question

The area of rectangular ground, having ratio of its side 5: 3. is 3375 m. If its
length is increased by 5 mand breadth is decreased by 5 m. then find its effect
on the a​

Answer 1

Given -

• Area of ground = 3375m²

• Ratio of length and breadth = 5 : 3

To find -

• Area of ground (after having changes in L and B).

Formula used -

• Area of rectangle.

Solution -

In the question, we are provided with the ratio of sides of a rectangular ground, and the area. And some changes are made in the L and B of the ground, and we need to find the area of the ground. For that we will first take the common ratio, then we will apply the formula of area of rectangle, then we will find the value of that common ratio, then we will multiply it with the L and B, after that we will obtain, new L and B, from that we will find the new area, so, Let's do it!

So -

Let the common ratio be termed as x

5 = 5x m

3 = 3x m

Area = 3375m²

Now -

We will find the value of x, by applying the formula of area of rectangle.

Area of rectangle = L × B

where -

L = Length

B = Breadth

On substituting the values -

Area = L × B

3375 = 5x × 3x

3375 = 15x²

x² = $\tt\dfrac{3375}{15}$

x² = 225

x = $\tt\sqrt{225}$

x = 15

Now -

We have obtained the value of x, so, now, we will multiply 5x and 3x with, 15, and that will be the new L and B of the rectangle, then we will find it's area, and it is also written, that 5m is increased in Length and 5m decrease in breadth, we will also do that.

So -

5x = 5 × 15 = 75m

3x = 3 × 15 = 45m

After increase and decrease in L and B -

New Length = 75m + 5m = 80m

New Breadth = 45m - 5m = 40m

At the end -

We will find the new area, by again applying the formula of area of rectangle.

Area of rectangle = L × B

New area = 80m × 40m

New area = 3200m²

Verification -

Of 1st area -

75m × 45m = 3375m²

3375m² = 3375m²

$\therefore$ The new area of rectangular ground is 3200m²

________________________________________________________

Answer 2

Answer:

Given :-

• Area of rectangular ground = 3375 m
• Ratio of side = 5:3
• Length increased by 5 and breadth decreased by 5 m

To Find :-

New area

Solution :-

As we know that

$\bf \pink{Area = l \times b}$

Let the sides be 5x and 3x.

$\tt \mapsto \: 3375 = 5x\times 3x$

$\tt \mapsto \: 3375 = 15x {}^{2}$

$\tt \mapsto \: \dfrac{3375}{15} = {x}^{2}$

$\tt \mapsto \: 225 = {x}^{2}$

$\tt \mapsto \: \sqrt{225} = x$

$\tt \mapsto \: 15 = x$

$\sf \: Length = 5x = 5(15) = 75 \: m$

$\sf \: Breadth = 3x = 3(15) = 45$

Now,

Length increases by 5 and breadth by 5

New Length = 75 + 5 = 80

New Breadth = 45 - 5 = 40

Now,

Let's find Area

$\bf \pink{Area = l \times b}$

$\tt \: Area =80 \times 40$

$\mathfrak \pink{Area = 3200 {m}^{2} }$

Formula :-

• Perimeter of rectangle = 2(l + b)
• Diagonal of rectangle = √length + Breadth
• Area of rectangle = length × Breadth
• Length = Area/Breadth
• Breadth = Area/Length