Math Problem Statement

The length of a rectangular garden is twice its width plus 2 meters. Walking around the garden once equals 68 meters. (a) Determine the length, width, and perimeter of the garden. (b) If the cost of grass per square meter is 20 taka, calculate the total cost to cover the entire garden with grass.

Solution

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Problem Transcription:

  1. একটি আয়তাকার মুলবাগানের দৈর্ঘ্য প্রস্থের দ্বিগুণ এবং ২ মি বেশি। মুলবাগানের চারদিকে একবার ঘুরে আসলে ৬৮ মিটার হাঁটা হয়।

    (a) দৈর্ঘ্য ও প্রস্থ মুলবাগানের পরিসীমা নির্ণয় কর।
    (b) মুলবাগানের প্রতি বর্গমি. ঘাস দিতে ২০ টাকা খরচ হয়, সমগ্র ঘাস দিতে কত টাকা খরচ হবে?


Translation:

  1. The length of a rectangular garden is twice its width plus 2 meters. Walking around the garden once equals 68 meters.

    (a) Determine the length, width, and perimeter of the garden.
    (b) If the cost of grass per square meter is 20 taka, calculate the total cost to cover the entire garden with grass.


Solution:

Part (a):

Let the width of the garden = xx meters.
Then, the length of the garden = 2x+22x + 2 meters.

The perimeter of the rectangular garden is given as: Perimeter=2×(Length+Width)=68meters.\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 68 \, \text{meters}.

Substituting the values: 2×((2x+2)+x)=682 \times ((2x + 2) + x) = 68

Simplify: [ 2 \times (3x + 2) = 68

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Math Problem Analysis

Mathematical Concepts

Linear equations
Geometry of rectangles
Area calculation

Formulas

Perimeter of a rectangle = 2 × (Length + Width)
Area of a rectangle = Length × Width
Cost = Area × Cost per square meter

Theorems

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Suitable Grade Level

Grade 6-8