For a pair of similar triangles, the angles made at \(Q\) is same in both the triangles \(PQR\) and \(LQJ\).
If the length of side \(QJ\) is 10 cm and \(QR\) is 5 cm, what is the ratio of their total areas?
To find the ratio of the total areas of the similar triangles \(\triangle PQR\) and \(\triangle LQJ\), we can use the property of similar triangles that states the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Given:
- Angle \(Q\) is the same in both triangles.
- Side \(QJ = 10 \, \text{cm}\) and side \(QR = 5 \, \text{cm}\).
Since the triangles are similar, the ratio of corresponding sides is:
\(\frac{QJ}{QR} = \frac{10}{5} = 2\)
The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides:
\(\left(\frac{10}{5}\right)^2 = 2^2 = 4\)
Therefore, the ratio of the areas of \(\triangle LQJ\) to \(\triangle PQR\) is 4.
Hence, the correct answer is 4.
Similar Questions
- The areas of two similar triangles $\Delta$XYZ and $\Delta$LMN are 49 cm$^2$ and 9 cm$^2$, respectively. If LM = 9 cm, then the length of XY is:
Triangles \(PQR\) and \(ABC\) are similar triangles. Triangle \(ABC\) have the following sides
\(AB = 12 \text{ cm}\),
\(AC = 15 \text{ cm}\),
\(CB = 21 \text{ cm}\).
Triangle \(PQR\) have the following sides:
\(PQ = 4 \text{ cm}\),
\(RQ = 7 \text{ cm}\).
What is the length of side \(PR\)?
- \(\Delta OPQ\) is similar to \(\Delta RST\). If the ratio of OP : RS is 3 : 5 and if PQ = 6 cm, then the length of ST is:
- Which of the following is the property of similar triangle?
- If in triangle \(\Delta\text{ABC}\) \(\text{AB}= 2\text{cm}\), \(\text{BC}=4\text{cm}\), and \(\text{AC}= 5\text{ cm}\) and in triangle \(\Delta\text{PQR}\) \(\text{PQ}= 12\text{cm}\), \(\text{QR}= 24\text{ cm}\), and \(\text{PR}=30\text{ cm}\), then triangles are:
- Two triangle are called similar if
- The areas of two similar triangles \(\Delta XYZ\) and \(\Delta LMN\) are \(49\ cm^2\) and \(9\ cm^2\), respectively. If LM = 9 cm, then the length of XY is:
Important Questions from Triangles, Congruence and Similarity
G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:
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:
