Two adjacent sides of rectangle are 5 x+6 and 2 x + 66. Find its area

1.	Two adjacent sides of rectangle are 5 x+6 and 2 x + 66. Find its area if its perimeter is 186 cm. *
Answer» → 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 : $\boxed{Area = lenth \times <klux>BREADTH</klux>}$ Perimeter of the rectangle : $\boxed{Perimeter = 2(<klux>LENGTH</klux> + Breadth)}$ → 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