Question

pls I beg u ans this Q plsss

Answer 1

EXPLANATION.

Each side of an equilateral triangle is x cm.

Each side is shortened by 12cm, 13cm, 14cm.

As we know that,

Pythagoras theorem.

⇒ H² = P² + B².

Hypotenuse > Perpendicular > Base.

Hypotenuse = (x - 12)cm.

Perpendicular = (x - 13)cm.

Base = (x - 14)cm.

Apply Pythagoras theorem, we get.

⇒ (x - 12)² = (x - 13)² + (x - 14)².

As we know that,

Formula of :

⇒ (x - y)² = x² + y² - 2xy.

Using this formula in the equation, we get.

⇒ x² + 144 - 24x = x² + 169 - 26x + x² + 196 - 28x.

⇒ x² + 144 - 24x = 2x² - 54x + 365.

⇒ 2x² - 54x + 365 - x² + 24x - 144 = 0.

⇒ x² - 30x + 221 = 0.

Factorizes the equation into middle term splits, we get.

⇒ x² - 17x - 13x + 221 = 0.

⇒ x(x - 17) - 13(x - 17) = 0.

⇒ (x - 13)(x - 17) = 0.

⇒ x = 13  and  x = 17.

⇒ x ≠ 13 [Because sides come negative].

⇒ x = 17.

Hypotenuse = (x - 12) = (17 - 12) = 5cm.

Perpendicular = (x - 13) = (17 - 13) = 4cm.

Base = (x - 14) = (17 - 14) = 3cm.

Answer 2

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