the length of the side of a triangle are 10cm 24cm 26cm find the length of the perpendicular let fall to side 26cm long from the opposite vertex
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Answered by
9
as you can see 10² + 24² = 26²
and hence the triangle is right angled.
and length of the perpendicular to the hypotenuse is given by 24*10/26
reason why: use coordinate geometry
equation of line of hypotenuse is x/24 + y/10 = 1.
and use the perpendicular distance formula of point (0,0) to this line.
the formula is :
if line is given by ax+by+c
then distance is |ax1+by1+c|÷(a²+b²) where x1 , y1 is the point from where the perpendicular is dropped onto the line.
you can also use sine rule
and hence the triangle is right angled.
and length of the perpendicular to the hypotenuse is given by 24*10/26
reason why: use coordinate geometry
equation of line of hypotenuse is x/24 + y/10 = 1.
and use the perpendicular distance formula of point (0,0) to this line.
the formula is :
if line is given by ax+by+c
then distance is |ax1+by1+c|÷(a²+b²) where x1 , y1 is the point from where the perpendicular is dropped onto the line.
you can also use sine rule
Answered by
17
as ( 10cm × 10cm +24cm ×24cm ) = 26cm × 26
it suited pythagorus theorem so this is a right angled triangle.
area of right angled triangle =1 /2 ×base ×height.
=1 / 2 × 10 ×24 square cm.
120 squar cm
if a perpendicular be drawn from opposite vertex to the another side then it would be base.
1 / 2 ×base ×height =120 squar cm
1 / 2 × 26 ×height =120 cm
height =120 / 13cm
it suited pythagorus theorem so this is a right angled triangle.
area of right angled triangle =1 /2 ×base ×height.
=1 / 2 × 10 ×24 square cm.
120 squar cm
if a perpendicular be drawn from opposite vertex to the another side then it would be base.
1 / 2 ×base ×height =120 squar cm
1 / 2 × 26 ×height =120 cm
height =120 / 13cm
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