Matt looks at the architectural plan of a four-walled room in which the walls meet each other at right angles. The length of one
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1. Draw an accurate picture of the triangle in
the coordinate axes, as shown in the attached picture.<span>
<span>2. Circumscribe a rectangle about the triangle, as shown in
the picture. The coordinates of the points M, N, T are easily identifiable as shown in the
picture.</span>
<span>3. The area of the triangle ABC is The area of
the rectangle - Area 1- Area 2- Area 3.</span>
Area 1 = 1/2(3*7)=21/2
Area 2 = 1/2(4*4)=1/2*16=8
<span>Area 3 = 1/2( 3*7)=21/2</span>
<span>Area 1+Area 2+Area 3=21/2+21/2+8=21+8=29 (units squared)</span>
<span>Area rectangle= 7*7=49 (units squared)</span>
<span>Answer: Area of triangle is 20 units squared.</span></span>
T<span>he area of a figure is the measure of the extent of a two dimensional figure which is usually measured as the square units of the dimensions of the figure.
For example, given a figure with dimensions, say k, the area of the figure is given by
.
</span>
<span>Given that o<span>ne similar figure has an area that is nine times the area of another.
Since the two figures are similar, it means that there areas will be proportional as their dimensions will be proportional.
Let the dimensions of the smaller figure be k and the larger figure is p times the smaller figure. Then the area of the smaller figure is and the area of the larger figure is 
.
Now, given that the area of the larger figure is nine times the area of the smaller figure, this means that:
</span>
Therefore, the larger figure must have dimensions that are 3 times the dimensions of the smaller figure.</span>
For example, given a figure with dimensions, say k, the area of the figure is given by
</span>
<span>Given that o<span>ne similar figure has an area that is nine times the area of another.
Since the two figures are similar, it means that there areas will be proportional as their dimensions will be proportional.
Let the dimensions of the smaller figure be k and the larger figure is p times the smaller figure. Then the area of the smaller figure is
Now, given that the area of the larger figure is nine times the area of the smaller figure, this means that:
</span>
Therefore, the larger figure must have dimensions that are 3 times the dimensions of the smaller figure.</span>
Answer:
Option C and E are correct.
The sequences which are arithmetic:
18, 5.5, -7, -19.5, -32,....
16, 32, 48, 64, 80
Step-by-step explanation:
Arithmetic sequence states that a sequence in which a common difference between each consecutive term is constant.
Common difference(d) = for every natural number n.
Option A:
-5, 5, -5, 5, -5, .....
5-(-5) = 5+5 = 10 ,
-5 -5 = -10 .....
Since, the common difference for the given sequence is not constant.
Option B:
96, 48, 24, 12, 6
48 -96 = -48
24-48 = -24 ....
Common difference for the given sequence is not constant.
Option C:
18, 5.5, -7, -19.5, -32,....
5.5-18 = -12.5
-7 -5.5 = -12.5 ....
∴Common difference for the sequence is constant.
Option D:
-1, -3, -9, -27, -81 ,....
-3 -(-1) = -3+1 = -2
-9-(-3) = -9+3 = -6 ....
∴Common difference for the sequence is not constant.
Option E:
16, 32, 48, 64, 80
32-16 = 16
48 - 32 = 16 and so on...
∴Common difference for the sequence is constant.
Therefore, the sequences which are arithmetic are:
18, 5.5, -7, -19.5, -32,....
16, 32, 48, 64, 80