Question

Two adjacent sides of rectangle are 5 x+6 and 2 x + 66. Find its area if its perimeter is 186 cm. *​

Answer 1

→ To Find :

The area of the rectangle ...

→ Given :

Given ,the adjacent sides of the triangle are :

• $\mathtt{5x + 6}$
• $\mathtt{2x + 66}$

Perimeter of the rectangle :

• $\mathtt{186 cm}$

→ We Know :

Area of the rectangle :

$\boxed{Area = lenth \times breadth}$

Perimeter of the rectangle :

$\boxed{Perimeter = 2(Length + Breadth)}$

→ Concept :

Let the given side i.e (5x + 6) and (2x + 66) be the length and breadth of the rectangle ...

• L = 2x + 66
• B = 5x + 6

So , by the given Perimeter and taken sides ,we can find the original length and breadth of the rectangle .

ATF (According to the Formula)

$\mathtt{2(l + b) = P_{r}}$

Where,

• l = length
• b = Breadth
• P = perimeter

Putting the value in the formula ,we get :

$\mathtt{\Rightarrow 2(2x + 66 + 5x + 6) = 186}$

$\mathtt{\Rightarrow 2(7x + 72) = 186}$

$\mathtt{\Rightarrow 14x + 144 = 186}$

$\mathtt{\Rightarrow 14x = 186 - 144}$

$\mathtt{\Rightarrow 14x = 42}$

$\mathtt{\Rightarrow x = \dfrac{42}{14}}$

$\mathtt{\Rightarrow x = \cancel{\dfrac{42}{14}}}$

$\mathtt{\Rightarrow x = 3}$

Putting the value of x in the length and breadth, we get :

• Length = 2x + 66

» 2(3) + 66

» 6 + 66

» 72

• Breadth = 5x + 6

» 5(3) + 6

»15 + 6

»21

Hence ,the length of the rectangle is 72 cm and the breadth of the rectangle is 23 cm.

→ Solution :

• Length = 72 cm
• Breadth = 21 cm

Area of rectangle :

$\mathtt{Length \times breadth}$

Putting the value in the formula, We Get :q

$\mathtt{\Rightarrow 72 \times 21}$

$\mathtt{\Rightarrow 1512 cm^{2}}$

Hence ,the area of the rectangle is 1512 cm ².

→ Additional information :

• Area of square = (side)²

• Surface area of square = 6(a)²

• Lateral surface area of square = 4(a)²

• Surface area of rectangle = 2(lb + bh + lh)

• Surface area of cuboid = 2(l + b)

Where ,

l = length

b = breadth

a = side

h = Height

Answer 2

$\large\mathcal\purple{\underbrace{QUESTION:-}}$

Two adjacent sides of rectangle are 5x+6 and 2x+66. Find its area if its perimeter is 186 cm.

$\large\mathcal\red{\underbrace{SOLUTION:-}}$

☞ It is given that,

There are two adjacent sides of a rectangle. And, Its Perimeter is 186cm.

☞ Let,

The Length = 2x+66 cm.

The Breadth = 5x+6 cm.

☞ Now, Formula Used :-

2(Length + Breadth) = Perimeter.

Put the values given.

➝ 2(5x + 6 + 2x + 66) = 186cm.

➝ 2(7x + 72) = 186cm.

➝ 14x + 144 = 186cm.

➝ 14x = 186 - 144.

➝ 14x = 42.

➝ x = 42/14 = 3.

☞ So, The Value Of X = 3.

Now,

Length = 2x+66 = 6 + 66 = 72cm.

Breadth = 5x+6 = 21cm.

☞ Now, Calculating Area.

Area Of Rectangle = Length × Breadth.

Put the values.

➝ Area = 72 × 21.

➝ Area = 1512cm²

Hence, Area is 1512 cm².