Question

A rectangular garden has an area of 84 m² and a perimeter of 38 m. Find its lengths and width.

Answer 1

SOLUTION :-

☯️ Let,

• Length Of Rectangle = L.

• Width Of Rectangle = W.

☯️ And Now,

• Area Of Rectangular Garden = 84m²

• Perimeter = 38m.

☯️ According To The Question,

L × W = 84 => (Equation 1)

And,

⇒ Perimeter = 2(L + B).

⇒ 38 = 2(L + W)

⇒ L + W = 19m.

⇒ L = 19 – W => (Equation 2)

We can substitute in Equation 1,

⇒ 84 = W × (19 - W)

⇒ 84 = 19W – W²

⇒ W² – 19W + 84 = 0.

Use the Method Of Splitting Middle Term.

⇒ W² – 12W + 7W + 84 = 0.

⇒ W(W – 12) – 7(W – 12) = 0.

⇒ (W – 12)(W – 7) = 0.

So, Width Of Rectangle = 12 or 7 cm.

Now, Put W = 7 in Equation 2.

⇒ L = 19 – 7.

⇒ L = 12cm.

So,

• Length Of Rectangle = 12cm.

• Width Of Rectangle = 7cm.