Question

If the perimeter and the area of rectangle is 34 and 60cm2.the find the the diagonal of the rectangle.(PLEASE HELP GUYS.)

Answer 1

Let's take the length as x and breadth as y.

Given,

perimeter = 34cm

=> 2( L + B)

=>2 ( x + y)

34 = 2( x+ y)

x + y = 17

x = 17 - y ....... (a)

area = 60 cm²

=>L × B

=> x × y

60 = xy

60/ y = x .........(b)

equating a and b,

17 - y = 60/ y

(17- y) y = 60

17y - y² = 60

-y² +17y - 60 = 0

y² -17y + 60 = 0

y² - 12y -5y +60 = 0

y(y - 12) -5 (y - 12) = 0

(y -5) (y-12) = 0

y -5 = 0 and y-12 = 0

y = 5 and y = 1

since there are 2 values of y,

taking y = 5. and taking y = 12,

x= 17 - y

x = 12 and x = 5

thus, x = 12 or 5

y = 5 or 12

Answer 2

$\huge\sf{\bold{\underline{\pink{Solution:}}}}$

$\sf\bold{\underline{Given\:that:}}$

• Perimeter of rectangle = 34 cm^2

• Area of rectangle = 60 cm^2

$\sf\bold{\underline{To\:find:}}$

• The diagonal of rectangle.

Let the length of the rectangle be x

$\implies$ 34 - 2x

Now, width will be :

$\implies$ $\frac{34-2x}{2}$ = 17-x

Area of the rectangle :

$17 - x = 17x - x {}^{2}$

$17x - x {}^{2} = 60$

$x {}^{2} - 17x + 60 = 0$

Value of x :

Roots are :- -5 and -12

$x {}^{2} - 5x - 12x + 60 = 0$

$x(x - 5) - 12(x - 5) = 0$

$(x - 5)(x - 12) = 0$

Therefore, x = 5 or 12.

We know that, the width would be less than the length.

Thus, the width will be :

$\implies$ 17 - 12 = 5cm

The length will be :

$\implies$ 12 cm.