In the given triangle, ∠aed ∼ ∠ abc, ad = 6.9, ae = 7.2, de = 5.2, and bc = 10.2. find the measure of bd and ce. round your answer to the nearest tenth.

The measure of side BD is 8.6  and The measure of side CE is 8.4  

Step-by-step explanation:

Given as :

The Triangle is ABC with side AB , BC , CA

And The points E  and D  is on the side AB and AC

So, AED is a Triangle

And Δ AED Δ ABC

The measure of side AD = 6.9

The measure of side AE = 7.2

The measure of side ED = 5.2

The measure of side BC = 10.2

Let The The measure of side EB = x

And The measure of side DC = y

So, From similarity property

= =

Or,   =

So, =

Or, 5.2 × ( 7.2 + x ) = 10.2 × 7.2

Or, 37.44 + 5.2 x = 73.44

Or, 73.44 - 37.44 = 5.2 x

∴ x =

I.e x = 6.9

Now in Δ BED

BE² + ED² = BD²

Or, 6.9² + 5.2² = BD²

Or, BD² = 74.65

∴  BD =

I.e BD = 8.64

Or, BD = 8.6

Similarly for y

=

Or,   =

Or, 5.2 × ( 6.9 + y ) = 10.2 × 6.9

Or, 35.88 + 5.2 y = 70.38

or, 5.2 y = 70.8 - 35.88

Or, 5.2 y = 34.5

∴  y =

I.e y = 6.6

Now in Δ CED

CD² + ED² = CE²

Or, 6.6² + 5.2² = CE²

Or, CE² = 70.6

∴  CE =

I.e CE = 8.40

Or, CE = 8.4

Hence The measure of side BD is 8.6  and The measure of side CE is 8.4  Answer

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

no solution

step-by-step explanation:

there is not enough information in the problem to solve.