Kim = 135/9 = 15 miles per week
Eric = 102/6 = 17 miles per week
Eric rode more.
Answer:
Refer the digram & explanation.
Step-by-step explanation:
<u>GIVEN :-</u>
- Tangents PQ & PR drawn to a circle with center O from an external point P.
<u>TO PROVE :-</u>
<u>CONSTRUCTION :-</u>
<u>FACTS TO KNOW BEFORE SOLVING :-</u>
- (Angle at which tangents are inclined to each other from the external point) + (Angle the tangents subtend at the center of the circle) = 180°.
<u>PROCEDURE :-</u>
∠QPR + ∠QOR = 180°
⇒ ∠QOR = 180° - ∠QPR
In ΔQOR , OQ = OR (∵ Radii of the circle are equal)
⇒ ΔQOR is an isosceles triangle (∵ OQ = OR i.e. two sides of the triangle are equal.)
⇒ ∠OQR = ∠ORQ (∵ In an isosceles triangle , the base angles are equal)
So,
∠QOR + ∠OQR + ∠ORQ = 180°
⇒ ∠QOR + 2∠OQR = 180° (∵ ∠OQR = ∠ORQ)
⇒ 180° - ∠QPR = 180° - 2∠OQR (∵ ∠QPR + ∠QOR = 180°)
⇒ -∠QPR = -2∠OQR (∵ Cancelling 180° from both the sides.)
⇒ ∠QPR = 2∠OQR (Proved)
Perimeter of the trapezoid
To find the perimeter, you add the lengths and widths of all the sides of the shop.
Hence, the perimeter is
P = (17 + 25 + 17 + 55) in = 114 in.
Therefore, the perimeter is 114 in.
Area
To find the area, you use the formula
![A=\frac{1}{2}(a+b)h](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28a%2Bb%29h)
where,
![\begin{gathered} a=25in \\ b=55in \\ h=8in \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%3D25in%20%5C%5C%20b%3D55in%20%5C%5C%20h%3D8in%20%5Cend%7Bgathered%7D)
Therefore,
![A=\frac{1}{2}(25+55)\times8=80\times4=320in^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%2825%2B55%29%5Ctimes8%3D80%5Ctimes4%3D320in%5E2)
Hence, the area of the trapezoid framed shop is 320in².
b) The frame has to do with perimeter and the glass would be the area because the area covers everything inside the frame.
Hence, the answer is Option D.
Answer: Circumference = 28.27cm