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Geometry/Perimeter of Garden

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QUESTION: Hello sir,

Sir iam not understanding this logical geometry question. Sirthe question is--:

The shape of the garden is rectangular in the middle and semi circular at both ends and the lenght of whole figure is 7m and breath of whole figure is 20m.Find the area and parimeteR OF THIS GARDEN.  Hint=(lenght of rectangle = 20-(3.5+3.5)

Sir in this related to hint iam having so much of confusions.
In this it is very difficult for me to understand this hint . sir please explain the soution in that manner that i can understand this sum and sir please dont think that i am asking this question for my homework. Sir the chapter which is contaning the above queztion is already teached and sir iam revising the chapters then this confusion created. Please expain in easy and lucid way

Thankyou

ANSWER: Hi Aishwarya,

This is a problem of subdivision.  To find the area of the garden, you need to find the area of the two semicircles plus the area of the rectangle.  To find the area of a circle, you need the radius.  To find the area of a rectangle, you need both the length and the breadth.

Let us begin with the semicircles.  Because the semicircles join to the length of the rectangle, the diameter of the semicircles equals the length of the rectangle.  So the semicircles have a diameter of 7, and you can divide that by 2 to get the radius: 3.5.

Now, the only missing parameter is the breadth of the rectangle.  Based on the arrangement of the figure, we can set up the below equation.

(Breadth of whole figure) = (Radius) + (breadth of rectangle) + (Radius)
(20) = (3.5) + (breadth of rectangle) + (3.5)

You can rearrange this equation to form the hint!  This tells you the breadth of the rectangle is 13.

Now that you have the radius (3.5), length of rectangle (7), and breadth of rectangle (13), you can use your formulas for area to determine the area of the entire garden.

Using the same parameters, you should be able to find the perimeter as well.

Feel free to ask a follow-up to see if you have obtained the correct answers.

Regards,
Azeem

---------- FOLLOW-UP ----------

QUESTION: Hello sir

IA AM NOT UNDERSTANDING THE LINE IN THE YOU ANSWER ---:

Now, the only missing parameter is the breadth of the rectangle.  Based on the arrangement of the figure, we can set up the below equation.
HOW BREATH IS MISSING THE BREATH IS 7 CM THERE ONLY HOW IT IS MISSING.

Answer
Hi,

The original is badly phrased.  For consistency, the hint should say "breadth of rectangle = 20-(3.5+3.5) ", instead of length.

Let me try to clarify by referring to the sides of the rectangle as "long" and "short".  The short side is 7m, given.  The radius, explained above, is half the short side, so 3.5m.  To find the long side of the rectangle, we must first look at the breadth of the whole figure (20), then subtract the radius from the left side (3.5) and the right side (3.5).

Hope this helps,
Azeem

Geometry

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

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CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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