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

Answer:

Let the base of the triangle be x cm.

Then, Altitude/ Perpendicular = (x - 7) cm.

Hypotenuse = 13 cm.           {given}

By using pythagoras theorem,

i.e. , (Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

Putting the values,

(13)^2 = (x-7)^2 + (x)^2

169 = x^2 + 49 - 14x + x^2

2x^2 - 14x - 120 = 0

Divinding the eq. by 2

x^2 - 7x - 60 = 0

x^2 + 5x - 12x - 60 = 0

x(x+5) - 12(x+5) = 0

(x+5)(x-12) = 0

x = -5, 12

Side length can never be negative. So we will neglect -5.

Thus, x = 12 cm = Base

Altitude/Perpendicular = x-7 = 12-7 = 5 cm.

Hope it helps..!!

Answer 2

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

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

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