Problem Analysis:
- We are given two similar triangles, $\Delta$XYZ and $\Delta$LMN.
- Their areas are Area($\Delta$XYZ) = 49 cm$^2$ and Area($\Delta$LMN) = 9 cm$^2$.
- A side length LM = 9 cm is given for $\Delta$LMN.
- We need to find the length of the corresponding side XY in $\Delta$XYZ.
Similar Triangles Area-Side Relationship
For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Mathematically, this is expressed as:
$ \frac{\text{Area}(\Delta \text{XYZ})}{\text{Area}(\Delta \text{LMN})} = \left(\frac{\text{XY}}{\text{LM}}\right)^2 $Calculating Side XY
- Substitute known values into the formula: $ \frac{49 \text{ cm}^2}{9 \text{ cm}^2} = \left(\frac{\text{XY}}{9 \text{ cm}}\right)^2 $
- Take the square root of both sides: $ \sqrt{\frac{49}{9}} = \frac{\text{XY}}{9 \text{ cm}} $ $ \frac{7}{3} = \frac{\text{XY}}{9 \text{ cm}} $
- Solve for XY: Multiply both sides by 9 cm: $ \text{XY} = \frac{7}{3} \times 9 \text{ cm} $ $ \text{XY} = 7 \times 3 \text{ cm} $ $ \text{XY} = 21 \text{ cm} $
Final Answer Determination
The calculated length of side XY is 21 cm.
Comparing this with the options:
- Option A: 21 cm
- Option B: 7 cm
- Option C: 49 cm
- Option D: 14 cm
The calculated length matches Option A.
Similar Questions
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 \(PR\)?
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?- \(\Delta OPQ\) 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:
