Question

The perimeter of a rectangle a picture frame is 66 inches. the length is 3 inches greater than the width the system of linear equations used to represent the situation shown below.

2X + 2Y = 66 and X +3 =Y

solve the system name dimension represented by each variable

Answer 1

Given:

• The perimeter of a rectangular picture frame is 66 inches [2X + 2Y = 66.]
• The length of the frame is 3 inches greater than the width [X + 3 = Y.]

To find: The dimensions.

Answer:

Formula to find the perimeter of a rectangle = 2 × (Length + Width)

We know that 2X + 2Y = 66. Simplifying it, we get:

2(X + Y) = 66

X + Y = 66/2

X + Y = 33

Now that we know the value of X + Y, and assuming X and Y to be the dimensions, let's substitute it into the formula to find the perimeter and verify it.

Perimeter = 2 × (X + Y)

66 = 2 × 33

It's verified.

Now, we also have the expression representing the length, which is X + 3 = Y.

X + Y = 33

X + 3 = Y

Let's add both expressions.

X + Y + X + 3 = 33 + Y

2X + Y + 3 = 33 + Y

2X = 33 - 3 + Y - Y

2X = 30

X = 30/2

X = 15

Hence, the width [X] is 15.

Substituting this value into the expression representing the length,

15 + 3 = Y

18 = Y

Hence, the length and breadth of the rectangular picture frame is 18 and 15 units respectively.

Hope it helps. :)