Carlos made a scale model of his house. The actual width is 30 feet, and the actual length is 45 feet. If the model has a width
of 6 inches, what is the length of his his model?
1 answer:
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Answer:
(i) The name of the part of the circle, OQ is a radius
(ii) The radius of the sector QOR is 21 cm
Step-by-step explanation:
The given figure is a sector of the circle O
∵ Any sector of a circle formed from 2 radii and an arc
∴ OQ is a radius
(i) The name of the part of the circle, OQ is a radius
The rule of the length of an arc of a circle is L = × 2 π r, where
- α is the angle of the sector
- r is the radius of the circle
∵ The length of the arc QR is 22 cm
∴ L = 22
∵ The measure of the angle of the arc is 60°
∴ α = 60°
∵ π =
→ Substitute them in the rule above
∵ 22 = × 2 ×
× r
∴ 22 = r
→ Divide both sides by
∴ 21 = r
(ii) The radius of the sector QOR is 21 cm
Answer:
Yes they are
Step-by-step explanation:
In the triangle JKL, the sides can be calculated as following:
- J(2;5); K(1;1)
=> JK =
- J(2;5); L(5;2)
=> JL =
- K(1;1); L(5;2)
=> KL =
In the triangle QNP, the sides can be calculate as following:
- Q(-4;4); N(-3;0)
=> QN =
- Q (-4;4); P(-7;1)
=> QP =
- N(-3;0); P(-7;1)
=> NP =
It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP
=> They are congruent triangles