Applying the Basic Proportionality Theorem
The problem involves a triangle ABC where a line segment DE is drawn parallel to the base BC, intersecting sides AB and AC at points D and E respectively. This setup allows us to use the Basic Proportionality Theorem (BPT), also known as Thales's Theorem.
Basic Proportionality Theorem (BPT)
The theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides proportionally. For triangle ABC with $DE \parallel BC$, the theorem gives us the following relationship:
$ \frac{AD}{DB} = \frac{AE}{EC} $Calculation Steps
- Identify Given Values:
- Ratio of segments on side AB: $AD/DB = 1/2$
- Length of segment AE on side AC: $AE = 5\text{ cm}$
- Apply the BPT Formula: Substitute the known values into the BPT equation: $ \frac{1}{2} = \frac{5\text{ cm}}{EC} $
- Solve for EC: Rearrange the equation to solve for the unknown length, EC. $ EC = 2 \times 5\text{ cm} $ $ EC = 10\text{ cm} $
Therefore, the length of EC is $10\text{ cm}$.
Similar Questions
In triangle ABC, a line segment DE is drawn through the centroid G, parallel to side BC. D lies on AB and E lies on AC. What is the ratio of the area of the smaller triangle ADE to the area of the trapezoid DECB?
A circle is circumscribed about a triangle. If one of the angles of the triangle is 120°, and the radius of the circumscribed circle is r, what is the length of the side opposite the 120° angle?
In △ABC and △XYZ, AB = XY, BC = YZ, and CA = ZX. By which congruence rule are the two triangles congruent?
Two triangles are similar with sides in the ratio 3:5. What is the ratio of their areas?
- A triangle with all its angles less than $90^\circ$ has its Orthocenter located where?
In \(\triangle ABC\), an angle bisector from A meets BC at D. If AD bisects \(\angle BAC\), and AB = AC, are \(\triangle ABD\) and \(\triangle ACD\) congruent? If so, by what rule?
In a triangle ABC, medians AD and BE intersect at G. If the length of median AD is 12 cm, what is the length of the segment AG?
Two right-angled triangular blocks, ABC and DEF, have ∠B = ∠E = 90°. If the lengths of the hypotenuses AC and DF are equal, and the sides AB and DE are equal, are the triangles congruent? If so, by what rule?
- A right-angled triangle ABC has legs AB=6 cm and BC=8 cm. An altitude BD is drawn from the vertex B to the hypotenuse AC. What is the length of the altitude BD?
- In $\triangle ABC$, a median AD is drawn to side BC. What is the ratio of the area of $\triangle ABD$ to the area of $\triangle ACD$?
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:
