Triangle Similarity Calculation
We are given that triangle ABC is similar to triangle EDF, denoted as \(\Delta ABC \sim \Delta EDF\). This similarity means that the ratio of their corresponding sides is constant.
The proportion of corresponding sides is:
\( \frac{AB}{ED} = \frac{AC}{EF} = \frac{BC}{DF} \)
Given Side Lengths:
- \(AB = 5 \text{ cm}\)
- \(AC = 7.5 \text{ cm}\)
- \(DF = 15 \text{ cm}\)
- \(ED = 12.5 \text{ cm}\)
Finding Remaining Sides:
First, determine the ratio of similarity using the known corresponding sides, AB and ED:
Ratio \(k = \frac{AB}{ED} = \frac{5}{12.5} = 0.4\)
This ratio \(k=0.4\) applies to all corresponding sides.
Calculating Side BC:
Use the similarity proportion \(\frac{AB}{ED} = \frac{BC}{DF}\):
\( \frac{5}{12.5} = \frac{BC}{15} \)
Solve for BC:
\( BC = 15 \times \frac{5}{12.5} = 15 \times 0.4 \)
\( BC = 6 \text{ cm} \)
Calculating Side EF:
Use the similarity proportion \(\frac{AB}{ED} = \frac{AC}{EF}\):
\( \frac{5}{12.5} = \frac{7.5}{EF} \)
Solve for EF:
\( EF = 7.5 \times \frac{12.5}{5} = 7.5 \times 2.5 \)
\( EF = 18.75 \text{ cm} \)
Sum of Remaining Sides:
The remaining sides of the two triangles are BC (from \(\Delta ABC\)) and EF (from \(\Delta EDF\)).
Calculate their sum:
Sum \(= BC + EF = 6 \text{ cm} + 18.75 \text{ cm}\)
Sum \(= 24.75 \text{ cm}\)
Similar Questions
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Important Questions from Triangles
What is \(AB + BC\) equal to?
In the given figure, if \(RS = 3\sqrt{3} \text{ cm}\) and \(RPS\) is an equilateral triangle, then find the value of \(QR\)
- In a right angled triangle, with angle at \(A\) being \(90^\circ\), the side \(AB\) is of length 3cm and \(BC\) is 12 cm. What is the length of side \(AC\)?
For a pair of similar triangles shown in the figure, the angles made at $B$ and $R$ are same in both the triangles $BAC$ and $RAQ$. If the ratio of the areas of the two triangles is 2:1, and if the area of $BAC$ is $100\text{ cm}^2$ then what is the area of $RAQ$ in sq.cm.?
- In a triangle $ABC$, the length of the side $AB$ is 2m, the angle at $C$ is $60^\circ$ and the angle at $B$ is $30^\circ$, what is the length of side $AC$?
