The perimeter of a rectangle is 42 metres and its diagonal is 15 metres. What are the lengths of its sides?

Given.

Perimeter = 42 m

Diagonal = 15 m

Formula used/Theory

⇒ Pythagoras theorem:-

Base² + Height² = Hypotenuse²

⇒ Perimeter of rectangle = 2(L + B)

If Perimeter of rectangle = 2(L + B)

Then;

2(L + B) = 42m

(L + B) =

(L + B) = 21m

Let L be x

Then, B is (21–x)

Then by Pythagoras theorem:-

Base² + Height² = Hypotenuse²

x² + (21–x)² = 15²

x² + (21)² + x²–2×x× 21 = 225

2x² – 42x + (441 – 225) = 0

2x² – 42x + 216 = 0

2(x² – 21x + 108) = 0

x² – 21x + 108 = 0

As comparing eq to ax² + bx + c = 0

x = = 12

x = = 9

if length is 12m

then, breadth = (21–12) = 9m

if length is 9m

then, breadth = (21–9) = 12m

Conclusion/Result.

Length of sides can be either (12,9) or (9,12)