Question

16. In the diagram below. ABC and ADE are similar. If AB -6, BD-4, and BC-7, then what is DE

Answer 1

The length of side DE in the similar triangles ABC and ADE is found by creating a proportion based on the given side lengths. The calculated length of side DE is 11.67 units (to two decimal places).

Step-by-step explanation:

The question is asking to find the length of side DE in the similar triangles ABC and ADE, given the lengths of some other sides in these triangles. When two triangles are similar, the lengths of their corresponding sides are proportional. We can set up a proportion using the given lengths to solve for DE:

AB / BC = AD / DE

We are given that AB = 6 and BC = 7. Since ADE and ABC are similar, AD is the sum of AB and BD, which means AD = 6 + 4 = 10. Now we can input these values into our proportion:

6 / 7 = 10 / DE

Multiplying both sides of the equation by DE and then by 7 to solve for DE, we get:

6 * DE = 10 * 7

DE = (10 * 7) / 6

DE = 70 / 6

DE = 11.67 (to two decimal places)

Answer 2

The measure of the side DE is
`(7)/(3)` unit .

Step-by-step explanation:

Given as Δ ABC and Δ ADE are similar :

The measure of side AB = 6 unit

The measure of side BD = 4 unit

The measure of side BC = 7 unit

Let The measure of side DE = x unit

From The property of similar triangle

`(\textrm The measure of side AB)/(\textrm The measure of side AD)` =
`(\textrm The measure of side BC)/(\textrm The measure of side DE)`

or.
`(\textrm 6)/(\textrm AB - AD)` =
`(\textrm 7)/(\textrm x )`

or, .
`(\textrm 6)/(\textrm 6 - 4)` =
`(\textrm 7)/(\textrm x )`

Or,
`(\textrm 6)/(\textrm 2)` =
`(\textrm 7)/(\textrm x )`

or, 3 × x = 7

∴ x =
`(7)/(3)`

Hence the measure of the side DE is
`(7)/(3)` unit . answer