Question

what is the lenght of ab

Answer 1

Answer:

7.35 cm

Step-by-step explanation:

See attachment for the extra lines drawn.

• Not that the information in the diagrams are diameters, therefore we need to divide by 2 to find the radius
• The question asked to find AB. From the diagram, AB = AM + MB

Find the radius

Diameter = 6 cm , radius = 6 ÷ 2 = 3 cm

Diameter = 4 cm , radius = 4 ÷ 2 = 2 cm

Diameter = 3 cm , radius = 3 ÷ 2 = 1.5 cm

Find the length MB:

PS is made up by the two radii 2 cm and 3 cm

⇒ PS = 2 + 3

⇒ PS = 5 cm

SR = Radius 3m - Radius 2 cm

⇒ SR = 1 cm

ΔPRS is a right angle triangle

RS² + RP² = SP²

1² + RP² = 5²

RP² = 25 - 1

RP² = 24

RP =√24

RP = 2√6 cm

MB = RP = 2√6 cm

Find the length AM:

OP is made up by the two radii 1.5 cm and 2 cm

⇒ OP = 1.5 + 2

⇒ OP = 3.5 cm

PQ  = MN - PN - MQ

PQ = 6 - 2 - 1.5

PQ = 2.5 cm

ΔOQP is a right angle triangle

OQ² + QP² = OP²

OQ² + 2.5² = 3.5²

OQ² = 3.5² - 2.5²

OQ² = 6

OQ = √6

AM = OQ = √6 cm

Find the length AB:

AB = AM + MB

AB = √6 + 2√6

AB = 3√6 = 7.35 cm

Answer: 7.35 cm