Question

if the perimeter and the diagonal of a rectangle is 18 cm and âš41 cm respectively. calculate the area of the rectangular field.

Answer 1

Question:

If the perimeter and the diagonal of a rectangle is 18 cm and √41 cm respectively. Calculate the area

of the rectangular field

(a) 25 cm²

(b) 29 cm²

(c) 18 cm²

(d) 20 cm²

Answer:

(d) 20 cm²

Step-by-step explanation:

Define x and y:

Let the length be x

and the breadth be y

Find area:

Area = Length x Breadth

Area = xy

Given perimeter = 18:

Perimeter = 2 (Length + Breadth)

2(x + y) = 18

x + y= 18 ÷ 2

x + y = 9 cm

Rewrite: (x + y)² :

(x + y)² = x² + y² + 2xy

x² + y² = (x + y)² - 2xy

Given diagonals = √41:

a² + b² = c²

x² + y² = (√41)²

x² + y² = 41

(x + y)² - 2xy = 41

Sub (x + y) = 9:

(x + y)² - 2xy = 41

(9)² - 2xy = 41

2xy = 81 - 41

2xy = 40

xy = 20

Answer: The area is 20 cm²