In ⊥∆ABC,
∠ABC = 90°.
AB is altitude,
BC is base AC is Hypotenuse
Let Base, BC = x cm.
if so considered, :
Altitude AB = (x – 7) cm.
Hypotenuse AC = 13 cm.
As per Pythagoras theorem,
In a right angled ABC,
AB2 + BC2 = AC2
(x – 7)2 + (x)2 = (13)2
x2 – 14x + 49 + x2= 169
2x2 – 14x + 49 = 169
2x2 – 14x + 49 – 169 = 0
2x2 – 14x – 120 = 0
x2 – 7x – 60 = 0
x2 – 12x + 5x – 6 0 = 0
x(x – 12) + 5(x – 12) = 0
(x – 12) (x + 5) =0
If x – 12 = 0, then x = 12
If x + 5 = 0, then x = -5
Positive value, x = 12
∴ Base, BC = x = 12 cm.
Altitude, AB = x – 7 = 12 – 7 = 5 cm.