Question

In the following figure, if ΔABC ∼ ΔDEF and their sides of lengths (in cm) are marked along them, then find the lengths of sides of each triangle.

Answer 1

Given, ΔABC ∼ ΔDEF

Then according to question,

`"AB"/"BC" = "DE"/"EF"`

⇒ `(2x - 1)/(2x + 2) = 18/(3x + 9)`

⇒ (2x – 1) (3x + 9) = 18 (2x + 2)

⇒ (2x – 1) (x + 3) = 6 (2x + 2)

⇒ 2x² – x + 6x – 3 = 12x + 12

⇒ 2x² + 5x – 12x – 15 = 0

⇒ 2x² – 7x – 15 = 0

⇒ 2x² – 10x + 3x – 15 = 0

⇒ 2x (x – 5) + 3 (x – 5) = 0

⇒ (x – 5) (2x + 3) = 0

Either x = 5 or `x = (-3)/2`, it is not possible

So, x = 5

Then in ΔABC, we have

AB = 2x – 1

= 2 × 5 – 1

= 9

BC = 2x + 2

= 2 × 5 + 2

= 12

AC = 3x

= 3 × 5

= 15

And in ΔDEF, we have

DE = 18

EF = 3x + 9

= 3 × 5 + 9

= 24

DE = 6x

= 6 × 5

= 30