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Monica [59]
3 years ago
5

The triangles are similar

Mathematics
2 answers:
Zina [86]3 years ago
5 0
20/5 = x /4   x =  80/5 = 16

x - 10 / 39 = 5/15 = 1/3
3x - 30 =  39
3x = 69
x = 23

(2x + 10 ) * 4 = 10 *(x + 3)

8x + 40 = 10x + 30
2x = 10 
x = 4

AE = 2(5) + 10  =  20






hoa [83]3 years ago
3 0

Answer:

Part 1) x=16\ units

Part 2) x=23\ units

Part 3) AE=20\ units

Part 4) x= 6.25\ units

Part 5) x=26.67\ in

Step-by-step explanation:

Part 1) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

so

In this problem

\frac{12}{3}=\frac{x}{4}\\\\3x=12*4\\ \\x=48/3\\ \\x=16\ units

Part 2) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

so

In this problem

\frac{36}{12}=\frac{39}{(x-10)}\\\\3(x-10)=39\\ \\x=(39/3)+10\\ \\x=23\ units

Part 3) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

so

In this problem

\frac{AB}{CD}=\frac{AE}{ED}

substitute the values

\frac{10}{4}=\frac{2x+10}{x+3}

2.5(x+3)=2x+10

2.5x+7.5=2x+10

2.5x-2x=10-7.5

0.5x=2.5

x=5\ units

AE=2x+10=2*5+10=20\ units

Part 4) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

so

In this problem

\frac{4}{5}=\frac{5}{x}\\ \\4x=5*5\\ \\ x=25/4\\ \\ x= 6.25\ units

Part 5) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

so

In this problem

\frac{30}{x}=\frac{45}{40}\\ \\45x=30*40\\ \\x=1,200/45\\ \\ x=26.67\ in



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