Question

http://prntscr.com/72uvr4
@perl

Answer 1

are you having trouble with part 1 ?

Answer 2

those two triangles are similar because they have two corresponding angles that are congruent

Answer 3

Δ ACD ~ Δ BCA
therefore
AC / BC = AD / BA note the order of the sides

Answer 4

I don' t know what to do :(

Answer 5

we can plug in the values given

Answer 6

we know AC is 4 ,

Answer 7

AC = 4, AD = 5 , AB = 8

AC / BC = AD / BA
4/ BC = 5 / 8

Solve for side BC, the unknown

Answer 8

6.5?

Answer 9

8*4 = 5*BC
32 = 5*BC
32/5 = BC
6.4 = BC

Answer 10

oops typo

Answer 11

Now what,what next?

Answer 12

@perl

Answer 13

because
Δ ACD ~ Δ BCA we have three ratios of sides
AC / BC = AD / BA = CD / CA

Answer 14

To find CD we can use either
AC/BC = CD/CA , or AD/BA = CD/CA

Answer 15

Now?

Answer 16

AC = 4, AD = 5 , AB = 8

AD/BA = CD/CA ->

5/8 = CD / 4

solve for CD

Answer 17

cross multiply:
4 *5 = 8 * CD

Answer 18

2.5?

Answer 19

correct

Answer 20

What about the area?

Answer 21

@perl

Answer 22

The formula for area of a triangle is 1/2 base x height

Answer 23

$$ \Large { \frac{A}{A'}=\frac{\frac12 b h }{\frac12 b' h' }

}$$

Answer 24

But,I was told to square the sides T_T

Answer 25

Thanks
Can you help me a bit more?

Answer 26

so it is enough to multiply the ratio of two sides, twice

Answer 27

in similar triangles, the ratio of two corresponding sides are equal

Answer 28

$$ \Large { \frac{A}{A'}=\frac{\frac12 b h }{\frac12 b' h' }= \frac{b}{b'} \cdot \frac{h}{h'} = \frac{b}{b'}\cdot \frac{b}{b'} = \left(\frac{b}{b'}\right)^2

}$$

Answer 29

note that h/h ' = b/b' = ratio of any two corresponding sides

Answer 30

now they want the ratio of the area of the *smaller* triangle to the *bigger* triangle

Answer 31

since side AD corresponds to side BA,

we have ratio of areas = (5 / 8)^2

Answer 32

25/64

Answer 33

Thanks

Answer 34

your welcome