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