QQuestion
In the given diagram, △ABC ∼ △EFG. If ∠ABC = ∠EFG = 60°, then the length of side FG is:
(a) 15 cm
(b) 20 cm
(c) 25 cm
(d) 30 cm
✓Answer
(a) 15 cm
Explanation:
Given, △ABC ∼ △EFG.
Therefore, corresponding sides are proportional.
\frac{AB}{EF}=\frac{BC}{FG}From the diagram, AB = 15 cm, EF = 75 cm and BC = 3 cm.
\frac{15}{75}=\frac{3}{FG}⇒ \frac{1}{5}=\frac{3}{FG}
⇒ FG = 3 × 5
⇒ FG = 15 cm
Related Questions
More ICSE Moderate level questions
In the given diagram, △ABC ∼ △PQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively, then: (a) △ABC ∼ △PQS (b) △ABD ∼ △PQS (c) △ABD ∼ △PSR (d) △ABC ∼ △PSR
In the given figure, ∠BAP = ∠DCP = 70°, PC = 6 cm and CA = 4 cm. Then PD : DB is: (a) 5 : 3 (b) 3 : 5 (c) 3 : 2 (d) 2 : 3
In △ABC, ∠ABC = 90°, AB = 20 cm and AC = 25 cm. DE is perpendicular to AC such that ∠DEA = 90° and DE = 3 cm, as shown. (a) Prove that △ABC ∼ △AED. (b) Find BC, AD and AE. (c) If BCED represents land on a map whose actual area is 576 m², find the scale factor of the map.
In the given figure, AC ∥ DE ∥ BF. If AC = 24 cm, EG = 8 cm, GB = 16 cm and BF = 30 cm: (a) Prove △GED ∼ △GBF (b) Find DE (c) Find DB : AB.
In the given diagram, △ADB and △ACB are two right-angled triangles with ∠ADB = ∠BCA = 90°. If AB = 10 cm, AD = 6 cm, BC = 2.4 cm and DP = 4.5 cm: (a) Prove that △APD ∼ △BPC. (b) Find the lengths of BD and PB. (c) Hence, find the length of PA. (d) Find area of △APD : area of △BPC.
Perimeters of two similar triangles are 27 cm and 16 cm. If the length of a side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle
If the lengths of three sides of two triangles are in proportion, then which type of triangle is this?
Two triangles are similar if their corresponding sides are ___.
In trapezium ABCD, BC ∥ AD and AD = 4 cm. Diagonals AC and BD meet at O such that AO/OC = DO/OB = 1/2. Find the length of BC.
In ΔABC, L and M are two points on the sides AC and BC respectively such that LM || AB and AL are (x - 2) units, AC = 2x + 3 units, BM = (x – 3) units and BC = 2x units. Determine the value of x.
DE ∥ BC of ΔABC where D and E are two points on AB and AC, respectively. If AD = 5 cm, DB = 6 cm, and AE = 7.5 cm, calculate the length of AC.
Assertion (A): If sin² A + sin A = 1, then cos⁴ A + cos² A = 1. Reason (R): 1 − sin² A = cos² A. (a) A is true, R is false. (b) A is false, R is true. (c) Both A and R are true, and R is the correct reason for A. (d) Both A and R are true, and R is not the correct reason for A.