If we have a right-angled triangle and the length of its right side is twice the length of the other right side, and if there is a rectangle inside this triangle such that the two vertices of the rectangle touch the right sides of the triangle. What is the relationship between the length of the rectangle and the width of the rectangle

Question

05-02-2024
Mathematics

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If we have a right-angled triangle and the length of its right side is twice the length of the other right side, and if there is a rectangle inside this triangle such that the two vertices of the rectangle touch the right sides of the triangle. What is the relationship between the length of the rectangle and the width of the rectangle

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toniand toniand · Answer 1 · 2024-02-05T13:59:46+01:00

Answer:

Let's denote the length of one of the right sides of the right-angled triangle as 'a'. According to the given information, the length of the other right side would be twice that, so it is '2a'.

Now, let's consider the rectangle inside the triangle. Since two of the vertices of the rectangle touch the right sides of the triangle, one of the sides of the rectangle would be parallel to the shorter right side of the triangle (length 'a'), and the other side would be parallel to the longer right side of the triangle (length '2a').

Let's denote the length of the rectangle as 'l' and the width as 'w'.

The length 'l' of the rectangle would be equal to the length of the longer right side of the triangle (2a). Therefore, l = 2a.

The width 'w' of the rectangle would be equal to the length of the shorter right side of the triangle (a). Therefore, w = a.

So, the relationship between the length 'l' and the width 'w' of the rectangle is l = 2w.

In other words, the length of the rectangle is twice the width of the rectangle in this particular scenario.

Step-by-step explanation:

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