Question

In the adjoining figure PQRS is a parallelogram such that PS= 3x cm, QR=21cm, QT=(5y-10)cm and ST=(3y + 2)cm find the values of x and y

Answer 1

Step-by-step explanation:

Area of parallelogram is 252 cm^{2}cm

2

, distance between the longer sides is 24 cm and the distance between the shorter side is 24 cm.

Step-by-step explanation:

Using heron's formula,

Diagonal SQ = 13 cm

⇒ s = \frac{Perimeter of PSQ}{2}

2

PerimeterofPSQ

\frac{\textrm{peremeter of PSQ}}{2}

2

peremeter of PSQ

⇒ s = \frac{54}{2}

2

54

= 27 cm

⇒ Area = \sqrt{27(27 - 21)(27 - 20)(27 - 13)}

27(27−21)(27−20)(27−13)

⇒ Area = 126 cm^{2}cm

2

Area of parallelogram,

⇒ Area = 252 cm^{2}cm

2

For distance,

⇒ 126 = 0.5 x 21 x h

So, distance between the shorter sides is,

⇒ h = 25.2 cm

Now,

⇒ 126 = 0.5 x 20 x h

So, distance between the longer distances,

⇒ h = 24 cm