Question

HELP

2. TRIANGLE ABC~TRIANGLE ADE; find x
B
A
20
15
E
2x + 3
C

Answer 1

x = 9

Explanation:

In similar triangles, the corresponding sides are in same proportion.

AB = AD + DB

= 20 + 8

=28

ΔABC ~ ΔADE,

`\sf (BC)/(DE)=(AB)/(AD)\\\\\\(2x + 3)/(15)=(28)/(20)\\\\\ 2x + 3=(28)/(20)*15`

`2x + 3 = 7` *3

2x + 3 = 21

Subtract 3 from both sides,

2x = 21 - 3

2x = 18

Divide both sides by 2,

x = 18 ÷ 2

x = 9

Answer 2

x = 9

Explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

`(BC)/(DE)` =
`(AB)/(AD)` ( substitute values )

`(2x+3)/(15)` =
`(20+8)/(20)` =
`(28)/(20)` ( cross- multiply )

20(2x + 3) = 15 × 28 = 420 ( divide both sides by 20 )

2x + 3 = 21 ( subtract 3 from both sides )

2x = 18 ( divide both sides by 2 )

x = 9