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The Perimeter of a Rectangle is 104 M and Its Area is 640 M². Find Its Length and Breadth. - Mathematics

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Question

The perimeter of a rectangle is 104 m and its area is 640 m². Find its length and breadth.

Solution

Let the length and the breadth of the rectangle be x m and y m.
Perimeter = 2(x + y) m
∴ 104 = 2(x + y)
x + y = 52
y = 52 – x
Area = 640 m2
∴ xy = 640
x(52 – x) = 640
x2 – 52x + 640 = 0
x2 – 32x – 20x + 640 = 0
x(x – 32) – 20 (x – 32) = 0
(x – 32) (x – 20) = 0
x = 32, 20
When x = 32, y = 52 – 32 = 20
When x = 20, y = 52 – 20 = 32
Thus, the length and breadth of the rectangle are 32 cm and 20 cm.

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(B) | Q: 6 | Page no. 71
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The Perimeter of a Rectangle is 104 M and Its Area is 640 M². Find Its Length and Breadth. Concept: Quadratic Equations.
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