Question

réponse :
8 la ferme de toit ci - contre a la forme dun triangle rectangle isocèle. déterminez la longueur de chacune des contre - fiches de cette ferme de toit.
contre - fiches
a
3.8 m
d
3.8 m
f
b
?
e
?
c

Explanation:

Step1: Identify the triangle type

The main triangle is isosceles right - angled (since it's a roof truss with \(AD = DF=3.8\) m and the overall triangle is isosceles right - angled). The counter - fiche triangles are also similar and we can use the mid - segment theorem or the property of similar triangles. In an isosceles right - angled triangle, if we consider the mid - points (the points \(B\), \(D\), \(E\), \(C\) seem to divide the sides proportionally), the length of the counter - fiche should be half of the length of \(AD\) (or \(DF\))? Wait, no. Wait, the main sides \(AF\) is \(AD + DF=3.8 + 3.8 = 7.6\) m? No, wait, the triangle is isosceles right - angled, so \(AD = DF = 3.8\) m, and the counter - fiche is a mid - segment. The mid - segment of a triangle is parallel to the third side and half as long. But in this case, if we consider the triangle formed by the counter - fiche, since the main triangle is isosceles right - angled, and the counter - fiche is connecting the mid - points (assuming \(B\) and \(E\) are mid - points), then the length of the counter - fiche is \(\frac{3.8}{2}\)? Wait, no, wait. Wait, the length of \(AD\) is \(3.8\) m, and the counter - fiche is a mid - segment of the triangle with base \(AD\) (or \(DF\))? Wait, maybe it's a mid - segment. The mid - segment theorem states that the segment connecting the mid - points of two sides of a triangle is parallel to the third side and half its length. If we consider the triangle where the two sides are \(3.8\) m each, and the counter - fiche is the mid - segment, then the length of the counter - fiche is \(\frac{3.8}{2}=1.9\) m? Wait, no, wait. Wait, maybe the counter - fiche is a mid - segment of the triangle with base equal to \(3.8\) m. Wait, let's re - examine. The triangle is isosceles right - angled, and the counter - fiche is a mid - segment. So if we have a triangle with two sides of length \(3.8\) m, and the counter - fiche is connecting the mid - points of the other two sides, then the length of the counter - fiche is \(\frac{3.8}{2}=1.9\) m. Wait, but maybe it's a mid - segment of the triangle with base \(3.8\) m. Let's think again. The total length of \(AF\) is \(AD + DF = 3.8+3.8 = 7.6\) m? No, \(AD\) and \(DF\) are each \(3.8\) m, so \(AF = 7.6\) m? No, that can't be. Wait, maybe \(AD = 3.8\) m, and the counter - fiche is a mid - segment, so its length is \(\frac{3.8}{2}=1.9\) m. Wait, let's do the calculation. If we have a triangle, and we draw a segment connecting the mid - points of two sides, the length of that segment is half the length of the third side. So if one of the sides is \(3.8\) m, then the mid - segment (counter - fiche) length is \(\frac{3.8}{2}=1.9\) m.

Step2: Calculate the length

Using the mid - segment theorem, if the length of the side of the triangle is \(l = 3.8\) m, and the counter - fiche is the mid - segment, then the length of the counter - fiche \(x=\frac{3.8}{2}\)
\(x = 1.9\) m

Answer:

The length of each counter - fiche is \(1.9\) m.