in a right-anled triangle,sides are a,b and hypotenuse is c.if h is the altitude drawn on hypotenuse,then a- h*h=ab b- h*h=a*a+b*b c- h=a+b d- 1/h*h=1/a*a+1/b*B
Asked by architsrivastava02
| 4th Sep, 2010,
10:35: AM
Expert Answer:
Dear Student,
Let ABC be the right angled triangle with angle B=90o, AB = a; BC =b and AC =c. Let the altitude h meets AC at D. Let CD = x. So, DA = c-x
Hence;
In triangle BDC and ABD:
x2 = b2 - h2......................... (1)
(c-x)2 = a2 - h2.....................(2)
Also,c2 = a2+b2..........................(3) (from right triangle ABC)
equation (2):
c2 + x2 - 2cx = a2 - h2
=> a2+b2 +b2 - h2 - 2cx = a2 - h2 (from equations 1 and 3)
=> x2 = b4 / c2
Substituting it in equation 1 and using equation 3, we get:
1/h2 = 1/a2 + 1/b2
which is the option d
Regards Topperlearning.
Dear Student,
Let ABC be the right angled triangle with angle B=90o, AB = a; BC =b and AC =c. Let the altitude h meets AC at D. Let CD = x. So, DA = c-x
Hence;
In triangle BDC and ABD:
x2 = b2 - h2......................... (1)
(c-x)2 = a2 - h2.....................(2)
Also,c2 = a2+b2..........................(3) (from right triangle ABC)
equation (2):
c2 + x2 - 2cx = a2 - h2
=> a2+b2 +b2 - h2 - 2cx = a2 - h2 (from equations 1 and 3)
=> x2 = b4 / c2
Substituting it in equation 1 and using equation 3, we get:
1/h2 = 1/a2 + 1/b2
which is the option d
Answered by
| 5th Sep, 2010,
10:48: PM
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