Question

The longer side of a parallelogram is 15.5 cm and the corresponding altitude is 12 cm , if the altitude corresponding to the shorter side is 20 cm find the shorter side.

Answer 1

$\bigstar$ According To Question ;

• Longer side of a parallelogram = 15.5 cm
• Corresponding altitude of Longer Side = 12 cm
• Altitude corresponding to the shorter side = 20 cm

$\rule{330}{2}$

Let ABCD is a parallelogram with the longer side AB = 15.5 cm and corresponding altitude AE = 12 cm. The shorter side is BC and the corresponding altitude is CF = 20 cm

We know that : Area of Parallelogram = Base × Height

• We have two altitudes and two corresponding bases

Shorter Side × Corresponding Altitude of Shorter Side = Longer Side × Corresponding Altitude of Longer Side which means BC × CF = AB × AE

$\longrightarrow$ BC × 20 cm = 15.5 cm × 12 cm

$\longrightarrow$ BC × 20 cm = 186 cm²

Hence Shorter Side of a Parallelogram is 9.3 cm

Answer 2

Step-by-step explanation:

Let ABCD is a parallelogram with the longer side AB = 15.5 cm and corresponding altitude AE = 12 cm. The shorter side is BC and the corresponding altitude is CF = 20 cm

We know that : Area of Parallelogram = Base × Height

We have two altitudes and two corresponding bases

Shorter Side × Corresponding Altitude of Shorter Side = Longer Side × Corresponding Altitude of Longer Side which means BC × CF = AB × AE

⟶ BC × 20 cm = 15.5 cm × 12 cm

⟶ BC × 20 cm = 186 cm²

⟶ BC = 186/20 cm = 9.3 cm

Hence Shorter Side of a Parallelogram is 9.3 cm