It is given that ΔABC ∼ ΔYZX and Ar ΔABC : Ar ΔXYZ = 256 : 25. If AB = 12 cm, BC = 10 cm, CA = 15 cm, then what is the value of YZ (in cm)?
15/4
The correct answer is 15/4.
Similarly, the ratio of corresponding altitudes would be $\frac{16}{5}$. Understanding the correspondence between vertices is critical. If the similarity was stated as ΔABC ∼ ΔXYZ, then AB would correspond to XY, BC to YZ, and CA to XZ. Always pay close attention to the order of vertices in the similarity statement.
Similar Questions
It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
In a triangle, if the angles are in the ratio 1 ∶ 2 ∶ 3, then the ratio of the corresponding sides is:
Given that Δ MAN and Δ CPT are congruent to each other such that ∠M = 75, ∠N = 65, ∠A = 40, ∠C = x/2, ∠P = 6y + 16. Find the value of (x – 5y).
If M is the mid-point of the side BC of ABC, and the area of ABM is 19 cm2 , then the area of ABC is:
In trapezium ABCD, AB∥DC. The sides AD and BC are produced to meet at E. AB = 15 cm, CD = 10 cm, AD = 4 cm and BC = 5 cm, then DE = ?
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In ΔABC, ∠A = 48°. AB and AC is extended to points D and E respectively, if the bisectors of angle CBD and angle BCE meet at point O, then ∠BOC is equal to:
Let ΔABC ~ ΔPQR and \(\frac{{ar\left( {{\rm{\Delta \;ABC}}} \right)}}{{ar\left( {{\rm{\Delta \;PQR}}} \right)}} = \frac{9}{{169}}\) . If AB = 12 cm, BC = 7 cm and AC = 8 cm, then PQ (in cm) is equal to:
The side BC Δ ABC is produced to D. The bisectors of ∠ABC and ∠ACD meet at E. If AB = AC and ∠BEC = 24º, then the measure of ∠ABC is:
Important Questions from Triangles, Congruence and Similarity
If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?
What is the area of quadrilateral ABCD?
It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
Sides of two similar triangles are in the ratio 4 ∶ 9. Area of these triangles are in the ratio:
If the ratio of corresponding sides of 2 similar triangles is 2 ∶ 3. Then the ratio of their corresponding altitude is :
