The perimeters of ∆ABC and ∆DEF are 30 cm and 18 cm respectively. ∆ABC ~ ∆DEF, BC and EF are corresponding sides. If BC =9 cm, then EF =__________ cm.

2.7

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5.4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D 5.4

Since ∆ABC ~ ∆DEF,
∴ $\frac{A B}{D E} = \frac{B C}{E F} = \frac{A C}{D F} = \frac{A B + B C + C A}{D E + E F + F D} \Rightarrow \frac{B C}{E F} = \frac{30}{18} = \frac{5}{3} \Rightarrow \frac{9}{E F} = \frac{5}{3} o r E F = \frac{9 \times 3}{5} \Rightarrow E F = \frac{27}{5} = 5.4 c m$
Hence, option B is the correct answer.

Suggest Corrections

Similar questions

The corresponding sides of two similar triangles ABC and DEF are BC = 9.1 cm and EF = 6.5 cm. If the perimeter of $Δ D E F$ is 25 cm, find the perimeter of $Δ A B C$ .

Construct a quadrilateral BDEF where DE=4.5 cm, EF=3.5 cm, FB=6.5 cm,and $∠ F = 50^{\circ}$ and $∠ E = 100^{\circ}$

Q. In the given figure, a circle touches the side DF of △EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the perimeter of △EDF is
(a) 9 cm
(b) 12 cm
(c) 13.5 cm
(d) 18 cm

In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30cm, find the perimeter of the quadrilateral ARPQ.

Q. ∆ABC ∼ ∆DEF and the perimeters of ∆ABC and ∆DEF are 30 cm and 18 cm respectively. If BC = 9 cm, then EF = ?
(a) 6.3 cm
(b) 5.4 cm
(c) 7.2 cm
(d) 4.5 cm

Join BYJU'S Learning Program

The perimeters of ∆ABC and ∆DEF are 30 cm and 18 cm respectively. ∆ABC ~ ∆DEF, BC and EF are corresponding sides. If BC =9 cm, then EF =__________ cm.

The correct option is D 5.4 Since ∆ABC ~ ∆DEF, ∴ABDE=BCEF=ACDF=AB+BC+CADE+EF+FD⇒BCEF=3018=53⇒9EF=53 or EF=9×35 ⇒EF=275=5.4 cm Hence, option B is the correct answer.