In the given figure, \(HI\), \(GF\), and \(DE\) are parallel lines. If \(DG = 6\), \(GH = 4\), and \(FI = 8\), then \(EF = ?\)
12
12 is correct.
Parallel lines cut two transversals in the same ratio (intercept theorem), so the segments on one transversal are proportional to the matching segments on the other: \(\dfrac{DG}{GH} = \dfrac{EF}{FI}\).
Substituting the given lengths: \(\dfrac{6}{4} = \dfrac{EF}{8}\).
Therefore \(EF = \dfrac{6 \times 8}{4} = 12\).
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?
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 \(\Delta DEF\)?
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?
