Answer :
Let one side of right – angled triangle be x m and other side be x + 4 m
On applying the Pythagoras theorem –
202 = (x + 4)2 + x2
400 = x2 + 8x + 16 + x2
400 = 2x2 + 8x + 16
2x2 + 8x – 384 = 0
x2 + 4x – 192 = 0
Using the splitting middle term – the middle term of the general equation is divided in two such values that:
Product = a.c
For the given equation a = 1 b = 4 c = – 192
= 1. – 192 = – 192
And either of their sum or difference = b
= 4
Thus the two terms are 16 and – 12
Difference = 16 – 12 = 4
Product = 16. – 12 = – 192
x2 + 16x – 12x – 192 = 0
x(x + 16) – 12(x + 16) = 0
(x + 16) (x – 12) = 0
x = 16 or x = 12
x cannot be negative
Base is 12m and other side is 12 + 4 = 16m
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