Question

In the rectangle WXYZ, XY + YZ = 17 cm, and XZ + YW = 26 cm. Calculate the length and breadth of the rectangle?

Answer 1

Let the length of the rectangle be “a” and the breadth of the rectangle be “b”.

XY + YZ = 17 cm

b + a = 17           ...(1)

In the right ∆WXZ,

XZ² = WX² + WZ²

(XZ)² = a² + b² 

XZ = `sqrt("a"^2 + "b"^2)`

Similarly WY = `sqrt("a"^2 + "b"^2)`

⇒ XZ + WY = 26

⇒ `2sqrt("a"^2 + "b"^2)` = 26

⇒ `sqrt("a"^2 + "b"^2)` = 13

Squaring on both sides

a² + b² = 169

(a + b)² – 2ab = 169

17² – 2ab = 169

⇒ 289 – 169 = 2ab

⇒ 120 = 2ab

⇒ ab = 60

a = `60/"b"`       ...(2)

Substituting the value of a = `60/"b"` in (1)

`60/"b" +"b"` = 17

b² – 17b + 60 = 0

(b – 2) (b – 5) = 0

b = 12 or b = 5

If b = 12

⇒ a = 5

If b = 6

⇒ a = 12

Length = 12 m and breadth = 5 m