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. :)
