Answer:
29.86 units
Step-by-step explanation:
In the triangle BIS, IT is the bisector of angle BIS,
Let BI = ST = x... (1)
By angle bisector property of a triangle, we have:
Therefore,
BI = ST =6.93
Perimeter of triangle BIS
= BI + IS + ST + BT
= 6.93 + 12 + 6.93 + 4
= 29.86 units
The original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m
<h3>How does dilation affect length, area, and volume of an object?</h3>Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.
So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:
<u><em>L = k × M</em></u>
where 'k' will be called as scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by <u><em>k²</em></u><em> </em>to get each other corresponding quantity from their similar figures' quantities.
<u><em>So </em></u><u><em>area </em></u><u><em>of </em></u><u><em>first figure </em></u><u><em>= k² × area of second figure</em></u>
Similarly,
<u><em>Volume </em></u><u><em>of first figure = k³ × volume of second figure.</em></u>
It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.
For this case, we're given that;
Let the scale fator of dilation be k.
Then:
<u><em>So area of pre-image = k² × area of dilated image</em></u>
Thus, we get:
(took positive root as scaling is done by non-negative factors as only magnitude matters mostly)
Thus, we get:
Height of pre-image = (1/3) × Height of dilated image (say h)
Thus, the original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m
Learn more about dilation here:
Refer to the attached image. Since one vertex is the origin and the other two lay on the coordinate axes, the triangle is a right triangle. This means that, if we consider AB to the be base, AC is his height, and vice versa.
Anyway, it means that the area is given by
Since AB is a horizontal segment and AC is a vertical segment, their length is given by the absolute difference of the non-constant coordinate: points A and B share the same x coordinate, so we subtract the y coordinates:
The opposite goes for AC: points A and C share the same y coordinate, so we subtract the x coordinates:
So, the area is
