Question

the perimeter and diagonal of a rectangle is 18m and 5m respectively. then its area is​

Answer 1

Answer: 28 m²

Step-by-step explanation:

Let the length be = x

Let the breadth be = y

Perimeter of the rectangle = 2(x + y) = 18 m

2(x + y) = 18 m

(x + y) = 18 m / 2

(x + y) = 9 m

Take square on both sides.

(x + y)² = (9 m)²

x² + y² + 2xy = 81 m²

x² + y² = 81 m² - 2xy

Length of the diagonal = 5 m

The diagonal makes a triangle with the sides.

According to Pythagoras Theorem,

x² + y² = (5 m)²

x² + y² = 25 m²

81 m² - 2xy = 25 m²

81 m² - 25 m² = 2xy

56 m² = 2xy

2xy = 56 m²

xy = 56 m² / 2

xy = 28 m²

Area of the triangle = Length * breadth = xy = 28 m²