Question

In rectangle WXYZ XY+YZ=17cm XZ+YW=26cm. calculate the length and breadth.

Answer 1

Hi friend
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Your answer
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In a rectangle WXYZ ,

Given that : -

XY + YZ = 17 cm

XZ + YW = 26 cm

To calculate : - Length and breadth of the rectangle.

We know that,

Diagonals of a rectangle are equal.

So, XZ = YW

Then, XZ = YW = 26/2 = 13 cm

Now,

In ∆XYZ ,

Let YZ = P , Then, XY = (17 - P).

Then, By Pythagoras theorem,
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(P)² + (17 - P)² = (13)²

=> P² + 289 - 34P + P² = 169

=> 2P² - 34P = 169 - 289

=> 2(P² - 17P) = - 120

=> P² - 17P = - 120/2

=> P² - 17P = - 60

=> P² - 17P + 60 = 0

=> P² - 12P - 5P + 60 = 0

=> P(P - 12) - 5(P - 12) = 0

=> (P - 12)(P - 5) = 0

Now,
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P - 12 = 0

=> P = 12 cm

Again,

P - 5 = 0

=> P = 5 cm

Now,
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YZ = P = 12 cm [Because , YZ is the length of the rectangle ,so we will assign it the greatest value of P]

Again, XY = (17 - P) = (17 - 12) cm = 5 cm [Because , XY is thee breadth .]

Note : - If we use P = 5 cm value then , the length YZ will be less than the breadth XY . That is why , we need to use P = 12 cm value .

HOPE IT HELPS