Question

If AB=4.4cm,AE=3.5cm and AD=5.5cm,find the length of the perpendicular from B to AD

Answer 1

If AB = 4.4 cm, AE = 3.5 cm and AD = 5.5 cm, then the length of the perpendicular from B to AD is 2.8 cm .

Step-by-step explanation:

Referring to the figure attached below, we have,  

ABCD is a parallelogram  and since the opposite facing sides of a parallelogram are equal in length, so

AB = CD = 4.4 cm  

AE = 3.5 cm

AD = BC = 5.5 cm

Let the perpendicular height from B to AD be BM

We know that the formula of the area of a parallelogram is given by,  

Area = Base × Altitude

Firstly, we have  

Side CD = 4.4 cm and the perpendicular height corresponding to this side, AE which is 3.5 cm.  

∴ Area = CD × AE = 4.4 × 3.5 = 15.4 cm²  

Now, considering the side AD which is 5.5 cm and the corresponding perpendicular height to this side is BM.  

∴ Area = AD × BM

⇒ 15.4 = 5.5 × BM

⇒ AD =   $\frac{15.4}{5.5}$

⇒ AD = 2.8 cm  

Thus, the length of the perpendicular height from B to AD i.e., BM is 2.8 cm.  

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Answer 2

Step-by-step explanation:

Step-by-step explanation:

Referring to the figure attached below, we have,

ABCD is a parallelogram and since the opposite facing sides of a parallelogram are equal in length, so

AB = CD = 4.4 cm

AE = 3.5 cm

AD = BC = 5.5 cm

Let the perpendicular height from B to AD be BM

We know that the formula of the area of a parallelogram is given by,

Area = Base × Altitude

Firstly, we have

Side CD = 4.4 cm and the perpendicular height corresponding to this side, AE which is 3.5 cm.

∴ Area = CD × AE = 4.4 × 3.5 = 15.4 cm²

Now, considering the side AD which is 5.5 cm and the corresponding perpendicular height to this side is BM.

∴ Area = AD × BM

⇒ 15.4 = 5.5 × BM

⇒ AD = \frac{15.4}{5.5}

5.5

15.4

⇒ AD = 2.8 cm

Thus, the length of the perpendicular height from B to AD i.e., BM is 2.8 cm.