Question

A right angle triangle having perimeter 120 cm has its two perpendicular sides in the ratio 5:12 . Find the lengths of its sides

Answer 1

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Answer 2

$\bf{\Huge{\underline{\boxed{\bf{\red{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}$

A right angled triangle having perimeter 120cm has two perpendicular sides in the ratio 5:12.

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

The length of its sides.

$\bf{\Large{\underline{\bf{\blue{Explanation\::}}}}}$

Let the ratio be R

$\bf{We\:have\begin{cases}\sf{The\:base\:of\:triangle=5R}\\ \sf{The\:perpendicular\:of\:triangle=12R}\\ \sf{The\:hypotenuse\:of\:triangle=H}\end{cases}}$

• $\bf{\Large{\underline{\sf{\orange{Using\:Pythagoras\:Theorem\::}}}}}$

→ [Hypotenuse]² = [base]² + [Perpendicular]²

→ [H]² = [5R]² + [12R]²

→ H² = 25R² + 144R²

→ H² = 169R²

→ H = √169R²

→ H = 13R

We know that perimeter of right angled Δ;

⇒ Side + Side + Side

$\bf{Here,\:side\:of\:triangle\begin{cases}\sf{First\:side=13R}\\ \sf{Second\:side=5R}\\ \sf{Third\:side=12R}\end{cases}}$

⇒ 13R + 5R + 12R = 120

⇒ 30R = 120

⇒ R = $\bf{\cancel{\frac{120}{30} }}$

⇒ R = 4

Thus,

The first side of Δ, 13×4 = 52cm.

The second side of Δ,5×4 = 20cm.

The third side of Δ,12×4 = 48cm.