Question

if a rectangle has one of it's sides as 30 cm, and the length of it's diagonal is 50 cm


How the answer of this is 1200 cm² ?​

Answer 1

✮ Correct Question :

• If a rectangle has one of its sides as 30 cm, and the length of its diagonal is 50cm, then what is its area

✮ Answer :

• Area of Rectangle = 1200 cm²

✮  Explanation :

• We know A Rectangle can be divided into 2 Right angled Triangles

Consider a Rectangle ABCD

• The Sides are AB , BC , CD , AD
• The Diagonals are AC , BD

Then :

• Δ ABC is formed

• Δ ADC is formed

According To Pythagoras Theorem :

(Hypotenuse)² = (Side)² + (Side)²

⇒ (AC)² = (AB)² + (BC)²

⇒ (50)² = (30)² + (BC)²

⇒ 2500 = 900 + (BC)²

⇒ 2500 - 900 =  (BC)²

⇒ 1600 =  (BC)²

⇒ √1600 =  √(BC)²

⇒ 40 =  BC

⇒ BC = 40 cm

Since Opposite sides are equal in a Rectangle no need to calculate other Triangle dimensions

Area of Rectangle = Length × Breadth

⇒ Area of Rectangle = 30 cm × 40 cm

⇒ Area of Rectangle = 30 × 40 cm²

⇒ Area of Rectangle = 1200 cm²