Question

The width of a rectangle measures (t-9u) centimeters, and its length measures (4t-4u) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

1) (2t-13u) cm
2) (2t-5u) cm
3) (8t-8u) cm
4) (8t-13u) cm

Answer 1

The perimeter of the rectangle with width (t-9u) cm and length (4t-4u) cm is calculated as P = 10t - 26u cm. However, this expression does not match any of the given options, indicating a potential error in the provided choices.

Step-by-step explanation:

The perimeter of a rectangle is calculated by adding together twice the width and twice the length, so the formula for the perimeter (P) is P = 2l + 2w. Given that the width (w) is (t-9u) centimeters and the length (l) is (4t-4u) centimeters, we apply the formula with these expressions:

P = 2(t-9u) + 2(4t-4u)

This simplifies to:

P = 2t - 18u + 8t - 8u

Combining like terms, we get:

P = (2t + 8t) - (18u + 8u)

P = 10t - 26u

So, the expression for the perimeter of the rectangle in centimeters is P = 10t - 26u cm, which doesn't match any of the provided options. It seems that there might be a mistake in the options provided. None of the options given accurately expresses the perimeter of the rectangle based on the provided dimensions.