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1 . 

 

Two triangles are similar. The perimeter and area of the smaller triangle are $2$. The perimeter of the larger triangle is $3$. What is the area of the larger triangle?

 

2. 

 

The areas of three of four triangular regions are given in the diagram. What is the area of the remaining region?

3. As shown in the diagram, \(PQ/QR=1/3.\) Find \([PAB]/[QAB].\)

4. If \(CE:EA:AD:DB=2:3:4:5,\) then what is  \([ACD]/[ABE]\)?

 Feb 16, 2019
 #1
avatar+10355 
+2

Two triangles are similar. The perimeter and area of the smaller triangle are $2$. The perimeter of the larger triangle is $3$. What is the area of the larger triangle?

 

laugh

 Feb 16, 2019
 #2
avatar+100439 
+2

2.

 

The two triangles at the bottom of the figure are under the same height.....similarly...the remaining triangles are also under the same height

 

The base of the bottom right triangle with an area of 5 has the same base as the triangle with an area of 25

Thus.....the height of the larger triangle must be 5 times that of the smaller one

 

Similarly....the base of the bottom left triangle with an area of 2 has the same base as the triangle with the unknown area....and the height of the unknown triangle is also 5 times that of this smaller triangle....so....its area = 10

 

 

cool cool cool

 Feb 16, 2019
 #3
avatar+100439 
+2

4.

 

[ ACD]  = (1/2)(AD)(AC) sin CAD

 

[ABE] = (1/2)(AE)(AB) sin EAB

 

Sin CAD  = Sin EAB

 

So

 

[ ACD  ] / [ ABE ]  =          (AD) (AC)          (4)(5)           20 

                                        _________ =    ______  =    ____

                                          (AE) (AB)          (3)(9)           27 

 

 

 

cool cool cool  

 Feb 16, 2019
 #5
avatar+644 
+1

For non-trig...

 

This was a hard one for me, too.

Derived from AoPS.

 

You are very welcome!

:P

CoolStuffYT  Feb 16, 2019
 #4
avatar+644 
0

Derived from AoPS.

This is the answer to #3.

 

You are very welcome!

:P

 Feb 16, 2019

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