Question

The perpendicular sides of a right triangle (in cm), are x and (x-7) and its hypotenuse is 13 cm. Then x =​

Answer 1

Answer:

12 cm

Step-by-step explanation

Let there be a right angled triangle ABC with the sides as shown above.

angle B = 90°

Therefore, by pythagoras theorem,

AB^2 + BC^2 = AC^2

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

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

2x^2 - 14x = 120

x^2 - 7x - 60 = 0

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

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

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

Therefore, x = 12 or x = -5

But Length is never negative

Therefore x is not = -5

Therefore, x = 12 cm