A triangle has sides (x-5) cm, 2x cm, and 2x cm. Its perimeter is 40 cm. Find the lengths of the sides. A rectangle's length is twice its width and its perimeter is 48 cm. Find the width. Jum has some

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Question 34a:
The triangle has sides $(x-5)$ cm, $2x$ cm, and $2x$ cm (indicated by the dash marks). The perimeter is 40 cm.

Step 1: Write the equation for the perimeter.
The perimeter is the sum of all sides.

$$(x-5) + 2x + 2x = 40$$

Step 2: Combine like terms.

$$(x + 2x + 2x) - 5 = 40$$ $$5x - 5 = 40$$

Step 3: Solve for $x$.
Add 5 to both sides:

$$5x = 40 + 5$$ $$5x = 45$$

Divide by 5:

$$x = \frac{45}{5}$$ $$x = 9$$

Step 4: Calculate the length of each side.
Side 1: $x-5 = 9-5 = 4$ cm
Side 2: $2x = 2(9) = 18$ cm
Side 3: $2x = 2(9) = 18$ cm

The lengths of the sides of the triangle are 4 cm, 18 cm, and 18 cm.

$$\boxed{\text{4 cm, 18 cm, 18 cm}}$$