In the given construction of a triangle ABC in which BC - 5 cm- - B- 60 - and AB - AC - 8 cm- what is the length of BD-

The length of BD is equal to the sum of the nbsp;sides AB and AC. The steps of construction of nbsp;a triangle when its base, a base angle and sum of othe ...

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Standard VII

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Humayun

In the given ...

Question

$In the given construction of a triangle ABC in which BC = 5 cm, ∠ B = 60^{\circ} and AB + AC = 8 cm, what is the length of BD?$

7 cm

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20 cm

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8 cm

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10 cm

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Solution

The correct option is C 8 cm
The length of BD is equal to the sum of the sides AB and AC.

The steps of construction of a triangle when its base, a base angle and sum of other two sides are given are :-

1. Draw base BC = 5 cm and construct ∠B = 60°.

2. With centre B and radius 8 cm (AB + AC = 8 cm), draw an arc to cut BX at D.

3. Join CD and draw the perpendicular bisector of CD to meet BD at A.

4. Join AC to get the required triangle ABC.

Hence, the length of BD is found to be 8 cm.

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(i) AB = 4.3 cm, BC = 5.4, CD = 5 cm, DA = 4.8 cm and $∠$ ABC = $75^{\circ}$ .

(ii) AB = 6 cm, CD = 4.5 cm, BC = AD = 5 cm and $∠ BCD = 60^{\circ}$

(iii) AB = 8 cm, BC = 5.4 cm, AD = 6 cm, $∠ A = 60^{\circ}$ and $∠ B = 75^{\circ}$ .

(iv) AB = 5 cm, BC = 6.5 cm, CD = 4.8 cm, $∠ B = 75^{\circ}$ and $∠ C = 120^{\circ}$

(v) AB = 6 cm = AC, BC = 4 cm, CD = 5 cm and AD = 4.5 cm.

(vi) AB = AD = 5 cm, BD = 7 cm and BC = DC = 5.5 cm

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In a right triangle ABC, ∠B = 90°.

(a) If AB = 6 cm, BC = 8 cm, find AC

(b) If AC = 13 cm, BC = 5 cm, find AB

Q. In which of the following cases can a right triangle ABC be constructed?
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In the given construction of a triangle ABC in which BC = 5 cm, ∠B=60∘ and AB + AC = 8 cm, what is the length of BD?

$In the given construction of a triangle ABC in which BC = 5 cm, ∠ B = 60^{\circ} and AB + AC = 8 cm, what is the length of BD?$