https://file.aiquickdraw.com/mathbot/file/1726438270548yc0jifv5.jpg

https://file.aiquickdraw.com/mathbot/file/1726438270549citw36xr.jpg

It seems like you've uploaded two images from a mathematics word problem assignment involving right triangles. Let me help break down what you're working on.

From the images:

1. **Right Triangle Properties:**
   - In the first image, you are asked to find the lengths of the sides of the lower triangle.
   - The provided values for the longer leg (48 ft), shorter leg (36 ft), and hypotenuse (60 ft) correspond to a **3-4-5 Pythagorean triple** scaled by 12, which fits perfectly since \(3^2 + 4^2 = 5^2\) and \(36^2 + 48^2 = 60^2\).

2. **Second Image:**
   - The setup involves two adjacent right triangles with a common leg, forming a larger triangle.
   - The hypotenuse of the lower triangle is \(x + 12\), and the short leg is \(x - 12\).
   - The hypotenuse of the upper triangle is 21 feet.

The problem is leading towards using the **Pythagorean Theorem** in both triangles to find the value of \(x\). Let me work through the problem for you step by step.

Would you like a detailed breakdown of how to solve this?

The sail on a sailboat is in the shape of two adjacent right triangles. One of the right triangles is on top of the other. The hypotenuse of the lower triangle and the short leg of the upper triangle share a common side. The sides of the upper right triangle are labeled 21 ft. The values for the long side, short side, and hypotenuse of the lower right triangle are x − 12, x, and x + 12, respectively. Find the lengths of the sides of the lower triangle and the total sail area.

Solve a problem involving two adjacent right triangles on a sailboat. Use the Pythagorean Theorem to find the side lengths of the lower triangle and calculate the total sail area. Learn step-by-step how to apply algebraic techniques and geometry in this practical example. Suitable for high school students in grades 9-12.

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