Question

5. Find the length of the diagonal of a rectangle whose sides are 16 m and 30 m.​

Answer 1

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Step-by-step explanation:

Let ABCD be a rectangle and AB and BC are theadjacent sides of length 30cm and 16cm respectively.

Let AC be the diagonal.In △CBA, using Pythagoras Theorm,

⟹(Perpendicular)² + (Base)² =

(Hypotenuse)²

⟹ (AB)² + (BC)² = (AC²)

⟹ (30)² + (16²) = (AC²)

⟹ (AC²) = 900 + 256

⟹ (AC²) = 1156

⟹ AB = ±34

⟹ AB = 34 [taking positive square root]Hence, the length of a diagonal of a rectangle is 34cm.