In the adjoining figure, AD = BD and DE || BC. If AC = 6 cm and DE = 4 cm, then the length of BC is :
4 cm
5 cm
6 cm
8 cm

Question

In the adjoining figure, AD = BD and DE || BC. If AC = 6 cm and DE = 4 cm, then the length of BC is : 1. 4 cm 2. 5 cm 3. 6 cm 4. 8 cm

KnowledgeBoat · Accepted Answer

Given, D is the mid-point of AB. By converse of mid-point theorem, A line drawn through the midpoint of one side of a triangle, and parallel to another side, will bisect the third side. In △ABC, Since, D is the mid-point of AB and DE // BC, thus : E is mid-point of AC. By mid-point theorem, The line segment joining the mid points of any two sides of a triangle is parallel to the third side and is equal to half of it. Since, D and E are the mid-points of AB and AC respectively. DE || BC ⇒ DE = BC ⇒ BC = 2 DE ⇒ BC = 2 × 4 ⇒ BC = 8 cm. Hence, option 4 is the correct option.

Mathematics

In the adjoining figure, AD = BD and DE || BC. If AC = 6 cm and DE = 4 cm, then the length of BC is :
4 cm
5 cm
6 cm
8 cm

Mid-point Theorem

Related Questions

D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. If BC = 10 cm, CA = 12 cm and AB = 17 cm, then the perimeter of the DEF is :
13 cm
19.5 cm
39 cm
None of these

D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. If BC = 12 cm, CA = 15 cm and AB = 18 cm, then the perimeter of the quadrilateral DEAF is :
45 cm
27 cm
30 cm
33 cm

In the given figure, BP and CQ are two medians of the △ABC. If BC = 12 cm, the length of QP =
4 cm
6 cm
8 cm
10 cm

Mathematics

In the adjoining figure, AD = BD and DE || BC. If AC = 6 cm and DE = 4 cm, then the length of BC is :4 cm5 cm6 cm8 cm

Mid-point Theorem

Related Questions

D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. If BC = 10 cm, CA = 12 cm and AB = 17 cm, then the perimeter of the DEF is :13 cm19.5 cm39 cmNone of these

D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. If BC = 12 cm, CA = 15 cm and AB = 18 cm, then the perimeter of the quadrilateral DEAF is :45 cm27 cm30 cm33 cm

In the given figure, BP and CQ are two medians of the △ABC. If BC = 12 cm, the length of QP =4 cm6 cm8 cm10 cm

In the adjoining figure, AD = BD and DE || BC. If AC = 6 cm and DE = 4 cm, then the length of BC is :
4 cm
5 cm
6 cm
8 cm

D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. If BC = 10 cm, CA = 12 cm and AB = 17 cm, then the perimeter of the DEF is :
13 cm
19.5 cm
39 cm
None of these

D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. If BC = 12 cm, CA = 15 cm and AB = 18 cm, then the perimeter of the quadrilateral DEAF is :
45 cm
27 cm
30 cm
33 cm

In the given figure, BP and CQ are two medians of the △ABC. If BC = 12 cm, the length of QP =
4 cm
6 cm
8 cm
10 cm