Question

If the perimeter of a rectangle is 34 cm and the area is 72 square cm, then what are the dimensions of the rectangle?

The width, or shorter side is ___ cm

The length, or longer side is___ cm

Answer 1

Solution-

Let the width and length of the rectangle be x and y respectively.

Now, according to question

The perimeter of a rectangle is 34 cm.

We know that the formula for

Perimeter of rectangle = 2×(length+ width)

So, 34 = 2×(y + x)

Reversing the sides.

Or 2(x + y) = 34

Dividing both sides by 2

Or (x+ y) = 34/2

Performing division

Or x + y = 17

Or y = 17 - x ....(1)

The area of rectangle is 72 square cm.

We know that the formula for

Area of reactangle = x×y

So, 72 = xy

Or xy = 72

Putting the value of y from equation (1) we get

x(17 - x) = 72

Or 17x - x² = 72

Or 17x - x² - 72

Or - x² +17x -72 =0

Solving it by factorisation method

-x² + 9x +8x - 72 =0

-x(x -9) +8(x-9) =0

(x -9(-x+8) =0

This gives x -9 =0 , -x +8=0

Or x =9 cm or x = 8 cm

Putting these values in equation (1) we get

y = 17 -9 = 8cm , y = 17 -8 = 9 cm

Since length is greater than width.

So,

The width, or shorter side is 8 cm and

The length, or longer side is 9 cm

Hence,

The width, or shorter side is 8 cm

The length, or longer side is 9 cm