Question

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

Answer 1

Answer:

let base be h then height = h-7

according to Pythagoras theorem

h² + (h-7)² = 13²

2h² -14h + 49 = 169

2h²-14h-120 = 0

h²-7h-60 = 0

h²-12h+5h-60=0

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

h=-5,12 ( discard -5 as length cannot be negative )

therefore h=12cm

altitude = h-7 = 12-7 = 5cm

Answer 2

Answer:

Let the base be x

And the altitude be (x-7)

By applying Pythagorean theorem

Hypotenuse^2= (side 1)^2 + (side 2)^2

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

${13}^{2} = {x}^{2} + (x - 7)^{2} \\ 169 = {x}^{2} + {x}^{2} - 14x + 49 \\ 169 = 2 {x}^{2} - 14x + 49 \\ {2x}^{2}  - 14x + 49 -169 = 0  \\ {2x}^{2} - 14 x - 120 = 0 \\ \frac{( {2x}^{2} - 14x - 120) }{2} = 0 \\ {x }^{2} - 7x - 60 = 0 \\ {x}^{2} - (12 - 5)x - 60 = 0 \\ {x}^{2} - 12x + 5x - 60 = 0 \\ x(x - 12) + 5 (x - 12) = 0 \\ (x + 5) (x - 12) = 0$

Therefore, x - 12 = 0 and x + 5 = 0

x - 12 = 0 and x + 5 = 0x = 12 and x = - 5

x - 12 = 0 and x + 5 = 0x = 12 and x = - 5We know that the value of the base cannot be negative.

Base = 12 cm, Altitude = 12 - 7 = 5 cm

Step-by-step explanation:

I hope this helps you