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

base 12cm and the hypotenuse is 5 cm

Answer 2

$\huge\star{\pink{\underline{\underline{\mathscr{Explanation:}}}}}$

______________________________

Given that:-

• The altitude of a right triangle is 7 cm less than its base.

• Hypotenuse of right angled triangle = 13cm

To find:-

• The other two sides.

______________________________

Let ,the base of the right triangle be x cm.

Given, the altitude of right triangle = (x – 7) cm

From Pythagoras theorem,

$\boxed{\red{Base^2+Altitude^2×=Hypotenuse^2}}$

∴ x^2 + (x – 7)2 = 132

$\hookrightarrow$x^2 + x2 + 49 – 14x = 169

$\hookrightarrow$ 2x^2 – 14x – 120 = 0

$\hookrightarrow$ x^2 – 7x – 60 = 0

 $\hookrightarrow$x^2 – 12x + 5x – 60 = 0

$\hookrightarrow$ x(x – 12) + 5(x – 12) = 0

$\hookrightarrow$(x – 12)(x + 5) = 0

Thus, either x – 12 = 0 or x + 5 = 0,

$\implies$ x = 12 or x = – 5

Since sides cannot be negative, x can only be 12.

$\huge\star$ Therefore, the base of the given triangle is 12 cm

$\huge\star$ The altitude of this triangle will be (12 – 7) cm = 5 cm.

$\huge{\blue{\underline{\mathrm{Hence,Solved}}}}$