What is the length of ab 3 circles in a rectangle/ questions?
Answers
Answer:
7.35 cm
Step-by-step explanation:
*See attachment for the extra lines drawn.
- Note 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
Hope it will be helpful to you
