Question

Perimeter of rectangle= 34 cm and area=60 sq.cm.what is the length of diagonal

Answer 1

Let the length of the rectangle be x then from the Perimeter the sum of the widths will be :

34 - 2x

The length of the width will be :

(34 - 2x)/2 = 17 - x

The area of the rectangle from the measurements will be :

x (17 - x) = 17x - x²

17x - x² = 60

x² - 17x + 60 = 0

Solving for x:

The roots are :

-5 and - 12

x² - 5x - 12x + 60 =0

x(x - 5) - 12 (x- 5) = 0

(x - 5)(x - 12) = 0

x = 5 or 12

We pick 12 since the width should be less than the length.

The width is thus :

17 - 12 = 5cm

Length is : 12cm

Answer 2

13 cm (answer)

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