Answer:
14.50 cm
Step-by-step explanation:
Based on the midsegment theorem:
The midsegment connecting two sides of triangle is parallel to the third side of the triangle and the length of the midsegment line is half the length of the third side parallel to the midsegment.
From the diagram ;
QR // ZY
XY = 2 * 2.93 = 5.86
RS // XZ
XZ = 2 * 2.04 = 4.08
QS // XY
XY = 2 * 2.28 = 4.56
The perimeter :
(XY + XZ + XY)
5.86 + 4.08 + 4.56
= 14.50 m
Part (a)
The angles would stay the same. This is because similar figures keep the same shape, but the size will shrink or grow.
A real world application is to simply move your head closer to the page and the figure will appear to get larger. The angles themselves stay the same but the side lengths will get larger.
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Part (b)
While the angles stay the same under a dilation operation, the side lengths do not. As the instructions state: "The side lengths are 3 times longer" (paraphrased).
So we multiply each side length in the diagram by 3
Refer to the diagram below. I've used the resize feature to enlarge the image to make figure DEFG
