Question

$\boxed{\checkmark} \: \sf{Question}$
Area of a rectangle is 325 cm².The perimeter of rectangle is 76 cm. Find its Dimensions.​

Answer 1

Answer:

$\boxed \checkmark \sf{answer} \\ \\ perimeter = 2(l + b)\\ 2(l + b) = 76 \\ l + b = 38 \\ l = 38 - b.....(1) \\ \\ area = lb \\ lb = 325...(2)\\ putting \: the \: value \: of \: l \: in \: (2) \\ (38 - b)b = 325 \\ 38b - {b}^{2} = 325 \\ \huge \bigstar \red{PLEASE \: \: MARK \: \: ME \: \: AS \: \: } \\ \huge \red{ THE \: \: BRAINLIEST \: \: AND \: \:} \\ \huge \red{FOLLOW} \bigstar$

Answer 2

Answer :

The length of the rectangle = 25 cm

The breadth of the rectangle = 13 cm

Step-by-step explanation :

Given :

• Area of a rectangle is 325 cm²
• The perimeter of rectangle is 76 cm.

To find :

the dimensions of the rectangle

Solution :

Let L cm be the length of the rectangle and B cm be the breadth of the rectangle.

First, let's get the relation between length and breadth of the rectangle.

Perimeter of the rectangle = 2 (length + breadth)

➙ Perimeter of the rectangle = 2 (L + B)

➙ 76 cm = 2(L + B)

➙ L + B = 76/2

➙ L + B = 38 cm

➙ L = (38 - B) cm

Now, substitute the value of length in area of rectangle formula. Then we'll get a quadratic equation. By solving the equation, we get the dimensions of the rectangle.

Area of the rectangle = length × breadth

➙ Area of the rectangle = L × B

➙ 325 cm² = (38 - B) (B)

➙ 325 = 38B - B²

➙ B² - 38B + 325 = 0

We'll solve this equation by factorization.

➙ B² - 25B - 13B + 325 = 0

➙ B(B - 25) - 13(B - 25) = 0

➙ (B - 25) (B - 13) = 0

➛ B - 25 = 0 ; B = 25

➛ B - 13 = 0 ; B = 13

So, the breadth of the rectangle is either 25 cm or 13 cm

Let B = 13 cm

L + B = 38

L + 13 = 38

L = 38 - 13

L = 25 cm

Therefore,

The length of the rectangle = 25 cm

The breadth of the rectangle = 13 cm