Question

if the length of diagonal of the rectangle and half its perimeter are 11 cm respectively and 13 cm is,what is its area?

Answer 1

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