Question

the area of a quadrilateral is 120cmsq. and the diagonal is 20 CM if the length of perpendicular from one vertex is 7 cm, find the length of the perpendicular from the vertex.
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Answer 1

Answer:

5cm

Step-by-step explanation:

Given

Area = 120 cm²

BD = 20 cm

CN = 7 cm

Area of the field = Sum of area of the 4 triangles

i.e. ΔAMD + ΔAMB + ΔCNB + ΔCND

⇒ 120 = (\frac{1}{2}

2

1

x DM x AM) + (\frac{1}{2}

2

1

x BM x AM) + (\frac{1}{2}

2

1

x BN x CN) + (\frac{1}{2}

2

1

x DN x CN)

⇒ 120 = (\frac{1}{2}

2

1

x DM x AM) + (\frac{1}{2}

2

1

x BM x AM) + (\frac{1}{2}

2

1

x BN x 7) + (\frac{1}{2}

2

1

x DN x 7)

Replacing

BM = BD - DM = 20 - DM

and

DN = DB - NB = 20 - NB

⇒ 120 = (\frac{1}{2}

2

1

x DM x AM) + (\frac{1}{2}

2

1

x (20 - DM) x AM) + (\frac{1}{2}

2

1

x BN x 7) + (\frac{1}{2}

2

1

x (20 - NB) x 7)

⇒ 120 = (\frac{1}{2}

2

1

x DM x AM) + 10 AM - (\frac{1}{2}

2

1

x DM x AM) + (\frac{7}{2}

2

7

BN) + 70 - (\frac{7}{2}

2

7

BN)

⇒ 120 = 10 AM + 70

⇒ 50 = 10 AM

⇒ AM = 5