Question

The perimeter of a rectangle is 28cm and its diagonals are 10cm. Find its area.

Answer 1

Let x be the length and y be the breadth.

Given perimeter = 28cm.

2(x + y) = 28

x + y = 14

y = 14 - x  -------- (1)

Now,

By Pythagoras s theorem.

x^2 + y^2 = 10^2

x^2 + y^2 = 100

x^2 + (14 - x)^2 = 100

x^2 + 196 + x^2 - 28x = 100

2x^2 - 28x + 196 = 100

2x^2 - 28x + 196 - 100 = 0

2x^2 - 28x + 96 = 0 

x^2 - 14x + 48 = 0

x^2 - 6x - 8x + 48 = 0

x(x - 6) - 8(x - 6) = 0

(x - 6)(x - 8) = 0

x = 6,8

y = 14 - 6, 14 - 8

   = 8,6 


Therefore the length = 8cm, breadth = 6cm.


Area of the rectangle = length * breadth

                                     = 8 * 6

                                     = 48cm^2.


Hope this helps!

Answer 2

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