Question

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

Answer 1

using. p. rule. base=x
x² =root (13)² - (x-7)²
x²= root 169- x²-49+14x
x²cnsl = 169-x²cnsl -14x
14x- 168 = 0
x = 168/ 14
x= 12

base =12. and other side is x-7.
12-7=5



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Answer 2

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

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

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