Question

The sides of a rectangle have the ratio 7:2. its perimeter is 207cm. Find the area

Answer 1

X - unit of length
w,l - the sides of a rectangle

7 : 2 ⇒ 7x : 2x

Perimeter: P = 207cm
Perimeter: P = 2w + 2l

therefore: 2w + 2l = 207    |divide both sides by 2

w + l = 103.5 (cm)

w : l = 7 : 2 ⇒ w : l = 7x : 2x ⇒ w = 7x; l = 2x

subtitute

7x + 2x = 103.5
9x = 103.5    |divide both sides by 9
x = 11.5 (cm)

7x = 7 · 11.5cm = 80.5cm
2x = 2 · 11.5cm = 23cm

w = 80.5cm; l = 23cm

Area = wl

Area: A = 80.5cm · 23cm = 1851.5cm²