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

Answer:

the two sides are 12 cm and 5 cm.

Explanation:

let base be=x

then altitude=x-7

h∧2=b∧2+p∧2

(13)∧2=(x-7)∧2+x∧2

169=x∧2-14x+49+x∧2

169 -49=2x∧2-14x

120=2x∧2-14x

2x∧2-14x-120=0

hope you can solve now

Answer 2

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

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

From Pythagoras theorem, we know,

Base2 + Altitude2 = Hypotenuse2

∴ x2 + (x – 7)2 = 132

⇒ x2 + x2 + 49 – 14x = 169

⇒ 2x2 – 14x – 120 = 0

⇒ x2 – 7x – 60 = 0

⇒ x2 – 12x + 5x – 60 = 0

⇒ x(x – 12) + 5(x – 12) = 0

⇒ (x – 12)(x + 5) = 0

Thus, either x – 12 = 0 or x + 5 = 0,  

⇒ x = 12 or x = – 5

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

Therefore, the base of the given triangle is 12 cm and the altitude of this triangle will be (12 – 7) cm = 5 cm.