in and isolation triangle ABC with ab = AC ,D and E are points on BC such that BE=CD .show that AD=AE?
2.a rhombus shaped field has green grass for 18 cows to graze if each side of the Rhombus is 30 metre and its longer diagonal is 48 metre how much area of grass field will each cow be getting?
please help me answer
Answers
1.we have ABC an isoceles triangle and AB=AC so angleB=angleC
now BE=CD
BE = BD + DE
CD = CE + DE
given BE = CD
BD + DE = CE + DE
BD = CE.............(1)
now in triangle ABD and triangle ACE
angle B =angle C (given)
AB =AC (given)
BD = CE (from eqn 1)
so triangle ABD is congruent to triangle ACE (siade angle side )
so AD = AE (corresponding part of congruent triangle or CPCT )
2.
When we will make a rhombus ABCD with a diagonal BD, we will get two triangles
triangle ABD
triangle BCD
Now , we will find the area od triangle ABD with Heron's Formula
s = a+b+c/2
= 30+30+48/2
= 108/2
= 54m
Area = root ( s(s-a)(s-b)(s-c) )
= root ( 54 (54-30) (54+30) (54+48) )
= root ( 54 * 24 * 24 * 6 )
= root ( 2*3*3*3*2*2*2*3*2*2*2*3*2*3) (through prime factorization)
= root ( 2*2*2*2*2*2*2*2*3*3*3*3*3*3)
= 432m2
Area of triangle BCD = 432*2
= 864m2
Area of grass field each cow will be getting = 864 / 18
= 48m2
Answer:
.we have ABC an isoceles triangle and AB=AC so angleB=angleC
now BE=CD
BE = BD + DE
CD = CE + DE
given BE = CD
BD + DE = CE + DE
BD = CE.............(1)
now in triangle ABD and triangle ACE
angle B =angle C (given)
AB =AC (given)
BD = CE (from eqn 1)
so triangle ABD is congruent to triangle ACE (siade angle side )
so AD = AE (corresponding part of congruent triangle or CPCT )
2.
When we will make a rhombus ABCD with a diagonal BD, we will get two triangles
triangle ABD
triangle BCD
Now , we will find the area od triangle ABD with Heron's Formula
s = a+b+c/2
= 30+30+48/2
= 108/2
= 54m
Area = root ( s(s-a)(s-b)(s-c) )
= root ( 54 (54-30) (54+30) (54+48) )
= root ( 54 * 24 * 24 * 6 )
= root ( 2*3*3*3*2*2*2*3*2*2*2*3*2*3) (through prime factorization)
= root ( 2*2*2*2*2*2*2*2*3*3*3*3*3*3)
= 432m2
Area of triangle BCD = 432*2
= 864m2
Area of grass field each cow will be getting = 864 / 18
= 48m2