if the length of diagonal of the rectangle and half its perimeter are 11 cm respectively and 13 cm is,what is its area?
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Given, diagonal of a rectangle is 13 cm and its perimeter is 34 cm.
Acc. To Question
2(x+y)=34 , where x=length of rectangle and y=width of rectangle.
or x+y=17
or y=17-x …..(A)
Since,diagonal of rectangle=13 cm (z cm)
In ΔXYZ,By P.G.T
x²+y²=z²
or y²=z²-x²
or y²=(13)²-x²
or y=√169-x²
or 17-x=√169-x² [From (A)]
Squaring both sides
(17-x)²=169-x²
or 289+x²-34x=169-x²
or 2x²-34x+120=0
or 2(x²-17x+60)=0
or x²-17x+60=0
or x²-12x-5x+60=0
or x(x-12)-5(x-12)=0
or (x-5)(x-12)=0
x=5 or x=12
And y=17-x
When x=5
y=17–5
y=12
When x=12
y=17–12
y=5
Now, Area of rectangular field=x×y
5×12=60 or 12×5=60
So, area of rectangular field=60 cm²
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