The lengths of the three sides of \(\Delta ABC\) are 6 cm, 4 cm, and 9 cm. Another triangle \(\Delta DEF\) is similar to \(\Delta ABC\), one side of which is 36 cm. What is the largest possible perimeter of \(\Delta DEF\)?
171 cm
171 cm is correct.
In similar triangles all sides are in the same ratio, so the perimeters are in that ratio too. The perimeter of \(\Delta ABC\) is \(6 + 4 + 9 = 19\) cm.
The perimeter of \(\Delta DEF\) is largest when the 36 cm side corresponds to the smallest side of \(\Delta ABC\), which is 4 cm. Scale factor: \(\dfrac{36}{4} = 9\).
Largest perimeter: \(19 \times 9 = 171\) cm (sides 54 cm, 36 cm and 81 cm).
Similar Questions
- In $\Delta ABC$ $\overline{PQ} \parallel \overline{AB}$. P and Q are on BC and CA respectively. If CQ : QA = 1 : 3 and CP = 4, then what is the value of BC?
- The altitudes of two similar triangles are 4 cm and 6 cm. If the area of the larger triangle is $36\text{ cm}^2$, what will be the area of the other one?
- The perimeters of two similar triangles $\Delta\text{XYZ}$ and $\Delta\text{LMN}$ are $48\text{ cm}$ and $32\text{ cm}$ respectively. If $\text{LM} = 12\text{ cm}$, then what is the length of XY?
- In $\Delta$ABC, DE||BC, intersecting AB at D and AC at E. AD : BD :: 2 : 3 and the area of trapezium BDEC is $63 \text{ cm}^2$. What is the area of $\Delta$ADE?
In the given figure, \(HI\), \(GF\), and \(DE\) are parallel lines. If \(DG = 6\), \(GH = 4\), and \(FI = 8\), then \(EF = ?\)
Important Questions from Triangles, Congruence and Similarity
In a $\Delta ABC$, $\angle C = (9/4) \angle B = (3/2) (\angle A+\angle B)$. Find the measure of the angles.
- 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 \(PR\)?
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?- In $\Delta ABC$ $\overline{PQ} \parallel \overline{AB}$. P and Q are on BC and CA respectively. If CQ : QA = 1 : 3 and CP = 4, then what is the value of BC?
