Unknown side length of two similar triangles can be found out by scale factor and any of the side lengths.
Step-by-step explanation:
The similarity is one of the criteria of triangles. Two triangles are similar when their respective sides are in similar ratio or proportion. In layman’s term, it can be understood as a condition in which two triangles have similar shapes but not similar sizes.
If ΔABC is similar toΔ XYZ, then their respective sides would be in proportion to each other.
This means AB/XY=AC/XZ=BC/YZ
This common ratio is often termed as “scale factor”
Hence any sides length can be found out if either of the terms (i.e. scale factor, side ) is given.
The polygon is a penthagon.
In a regular polygon with n sides, the sum of the interior angles is
But we also know that each interior angle has a measure of 108, and of course there is a total of n angles. So, we also know that the sum of the interior angles is
Since we have two expressions for the same quantity, these expressions must equal each other:
To solve for n, let's start by expanding the left hand side:
Now move all terms involving n to the left hand side, and all constants to the right hand side:
Simplify the right hand side:
And finally, divide both sides by 72:
Answer:
<u>384</u>
The step-by-step explanation for <u>HEIGHT</u> first:
<u>8</u> cm is the height
step-by-step explanation:
v = · b · h
v = ( 12 · 12 ) ( 8 )
v = ( 144 ) ( 8 )
v = <u>384 cm³</u>
Answer:
A. 48
Step-by-step explanation:
The ratio of the area of rectangle ABCD to rectangle EFGH = the square of the ratio of the corresponding linear measurements of both shapes
Thus:
Area of ABCD/Area of EFGH = AB²/EF²
Area of ABCD = L*W = 18*24 = 432
Area of EFGH = 6*x = 6x
AB = 18
EF = 6
Therefore:
432/6x = 18²/6²
432/6x = 324/36
72/x = 9
Cross multiply
9x = 72
x = 72/9
x = 8
Area of EFGH = 6x
Plug in the value of x
Area of EFGH = 6(8) = 48
Answer:
Step-by-step explanation:
<em> will multiply the first equation with -2</em>
-2x-10y=-40
i will add it now to the second equation
-2x-10y=-40
2x-7y=9
-17y=-31
y=31/17
and x=185/17