EXAMPLE 15 ÎABC is a right triangle in which C-90Â° and CDIAB. If

1.	EXAMPLE 15 ÎABC is a right triangle in which C-90Â° and CDIAB. IfBC = a, CA = b, AB = c and CD = p then prove that)cp = ab(ii)[CBSE 1997C, '98, '99, '02]2
Answer» 1.Area is 1/2 base * height . So for the same triangle area can be 1/2ba and can be 1/2pc. Hence cp = ab 2 . From above p2 = a2b2/c2 1/p2 = c2/ a2b2 but for right triangle c2 = a2 +b2 Hence 1/p2 = (a2+b2)/ a2b2 Hence 1/p2 = 1/a2+1/b2 please like my answer if you find it useful

EXAMPLE 15 ÎABC is a right triangle in which C-90Â° and CDIAB. IfBC = a, CA = b, AB = c and CD = p then prove that)cp = ab(ii)[CBSE 1997C, '98, '99, '02]2

Answer»

1.Area is 1/2 base * height . So for the same triangle area can be 1/2*b*a and can be 1/2*p*c. Hence cp = ab

2 . From above p2 = a2b2/c2

1/p2 = c2/ a2b2

but for right triangle c2 = a2 +b2

Hence 1/p2 = (a2+b2)/ a2b2

Hence 1/p2 = 1/a2+1/b2

please like my answer if you find it useful