A campsite in the shape of a rectangle FGHI has sides (3x + 6) m and (x+1) m and the length of the diagonal FH is (4x+1) m. Find the area of the campsite

168 m²

Step-by-step explanation:

A rectangle is a quadrilateral (four sides) with two pairs of equal opposite sides. All the four angles in a rectangle are equal to 90°.

Given the sides of rectangle FGHI as (3x + 6) m and (x+1) m and the diagonal as (4x + 1) m.

Hence, from Pythagoras theorem:

(4x + 1)² = (3x + 6)² + (x + 1)²

16x² + 8x + 1 = (9x² + 36x + 36) + (x² + 2x + 1)

16x² + 8x + 1 = 10x² + 38x + 37

16x² + 8x + 1 - (10x² + 38x + 37) = 0

6x² - 30x - 36 = 0

6(x² - 5x - 6) = 0

x² - 5x - 6 = 0

x² - 6x + x - 6 = 0

x(x - 6) + 1(x - 6) = 0

(x + 1)(x - 6) = 0

x = -1 or x = 6

since x cannot be negative, therefore x = 6

Sides are (3x + 6) = 3(6) + 6 = 24 m

(x + 1) = 6 + 1 = 7 m

Diagonal = 4x + 1 = 4(6) + 1 = 25 m

Area of camp site = side * side = 24 m * 7 m = 168 m²