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 Triangles EFG and QRS are similar. The length of the sides of EFG are 144, 128, and 112. The length of the smallest side of QRS is 280, what is the length of the longest side of QRS? (draw a diagram and solve)answer choices360240290340

Sagot :

The length of the sides of EFG are 144 cm, 128 cm and 112 cm. And length of the longest side of QRS is 360 cm.

A triangle is a polygon with three sides and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is represented as ΔABC.

In Euclidean geometry, any three points, if not collinear, define a unique triangle and, at the same time, a unique plane (that is, two-dimensional Euclidean space). That is, there is only one plane containing this triangle, and all triangles are contained in one plane. If all geometries were just Euclidean planes, there would be only one plane and all triangles would be in it. But this is not the case in high dimensional Euclidean space. This article is about triangles in Euclidean geometry, specifically the Euclidean plane, unless otherwise stated.

According to the question:

Triangles EFG and QRS are similar

So EF/QR = FG/RS = EG/QS

Therefore,

The length of the sides of EFG are 144 cm, 128 cm and 112 cm.

Here, 112 is smallest side of triangle EFG  

Let, the smallest side of EFG  be EF so QR is also the smallest side of triangle QRS i.e. QR = 280 cm & other sides be assumed "x" & "y"

Now,

   112/280 = 144/x = 128/y

⇒ 2/5 = 144/x = 128/y

Taking first two, we get

x = 360 cm

Now,

Taking first and third , we get ,

y = 320 cm

So others two sides of triangle QRS are 320 cm & 360 cm.

And length of the longest side of QRS is 360 cm.

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