Math, asked by musadurrani, 1 month ago

A stage has an area of 1,298 square feet and a perimeter of 162 feet. What are the dimensions of the stage?

Answers

Answered by himanshuthegreat456
0

Answer: The dimensions of the stage is 22 feet and 59 feet

Step-by-step explanation:

As we do not know if the stage is a rectangle or a square, we'll consider the stage to be a rectangle, as square is the special case of a rectangle.

Let's consider the dimensions to be X and Y.

Therefore,

X*Y = 1298 (area of rectangle is L * B) ------------------------------------------- (1)

2(X+Y) = 162 (Perimeter of rectangle is 2(L+B) ------------------------------- (2)

=> (X+Y) = 162/2 = 81 -------------------------------------------------------------------- (3)

Now we have the values of X+Y and X * Y, so we need to find the value of X-Y in order to find the value of X and Y

Squaring both the sides in (3)

Therefore,

(X+Y)² = 81²

X²+Y²+2XY = 81²                             [(a+b)² = a²+b²+2ab]

Subtracting 4XY both the sides,

Therefore,

X²+Y²+2XY-4XY = 81²-4XY

X²+Y²-2XY = 81²-4XY

(X-Y)² = 81²-4XY                            [(a-b)² = a²+b²-2ab]

(X-Y)² = 81² - 4(1298)                     [ substituting the value of XY ]

(X-Y)² = 6561 - 5192

(X-Y)² = 1369

Rooting both the sides,

Therefore,

X-Y = 37 --------------------------------------------------------------- (4)

Adding (3) and (4)

X+Y+X-Y = 37+81

2X = 118

X = 59

Substituting the value of X in (4)

Therefore,

59-Y = 37

Y = 59-37 = 22

The dimensions of the stage is 22 feet and 59 feet

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