Question

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

Answer 1

Step-by-step explanation:

Given:

XY+YZ=17cm

XZ+YW=26cm

let XY be a

then YZ will be 17-a

let XZ be b

then YW will be 26-b

proof:

In triangle XYZ

${xz}^{2} = {zy}^{2} + {xy}^{2}$

(By Pythagoras theorem)

so,by substituting the given and assumed in the theorem we get,

b^2=289+2a^2-34a. (1)

In triangle WZX

${zx}^{2} = {wz}^{2} + {xz}^{2}$

(By Pythagoras theorem)

so,by substituting the given and assumed in the theorem we get,

676+b^2-52b=2a^2+289-34a

now by substituting (1) in the above we get,

676=52b

b=13

Now substitute b in (1)

we get,

a^2-17a+60=0

by solving we get,

a=3

so therefore, breadth=3

and length=17-a

=14