Question

If the perimeter and diagonal of a rectangle are 14 cm and 5 cm respectively, find its area.

Answer 1

Answer: 12 cm²

Step-by-step explanation: given below

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Answer 2

The area of rectangle is 12 square cm.

Step-by-step explanation:

We are given the following in the question:

Perimeter of rectangle = 14 cm

Diagonal = 5 cm

Let l be the length and b be the breadth of the rectangle.

Perimeter of rectangle =

$2\times (l + b) = 14\\l + b = 7$

The diagonal and sides of rectangle form a right angled triangle. Thus, by Pythagoras theorem

$l^2 + b^2 = (5)^2\\l^ + b^2 = 25$

Now,

$(l+b)^2 = (7)^2\\l^2 + 2lb + b^2 = 49\\2lb + 25 = 49\\2lb = 24\\lb = 12$

Area of rectangle =

$lb = 12\text{ square cm}$

The area of rectangle is 12 square cm.

#LearnMore

If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle.

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