Question

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find
the other two sides.​

Answer 1

Step-by-step explanation:

Solution

• Let's consider that the Base of right traingle is x cm.

• And, Altitude be (x - 7) cm.

$\underline{\bigstar\:\textsf{By Using Pythagoras Theorem \ :}}$

$\star$ Base² + Altitude² = Hypotenuse²

$:\implies\tt x^2 + (x - 7)^2 = 13^2 \\\\\\:\implies\tt x^2 + x^2 + 49 - 14x = 169\\\\\\:\implies\tt 2x^2 - 14x - 120 = 0\\\\\\:\implies\tt x^2 - 7x - 60 = 0\\\\\\:\implies\tt x^2 - 12x + 15x - 60 = 0\\\\\\:\implies\tt x(x - 12) + 5(x - 12) = 0\\\\\\:\implies\tt (x - 12) (x + 5) = 0 \\\\\\:\implies\tt x - 12 = 0\\\\\\:\implies\tt x = 12\\\\\\:\implies\tt x + 5 = 0\\\\\\:\implies\tt x = -5$

$\therefore\:\underline{\textsf{Ignoring negative value, Base \& Altitude is \textbf{12, 5 cm}}}.$

Answer 2

Answer:

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