The lenghth of a rectangle is  greater than the width.

The length of the base of an isosceles traingle is and the lengths of the other two sides are greater than the width of the rectangle.

a.

Draw the figures :

Rectangle :                                                                             Isosceles triangle :

b.

Find the expression of perimeter of the triangle and rectangle :

Rectangle :

The perimeter of the rectangle is .

Here, and .

                            (Orginal formula)

                    (Substitute and )

                         (Simplify)

The perimeter of the rectangle is (or) .

Isosceles triangle : 

The perimeter of the isosceles triangle is .

Here, and .

                                 (Orginal formula)

                          (Substitute and )

                             (Multiply)

                                    (Simplify)

The perimeter of the isosceles triangle is (or) .

c.

Find the width of the rectangle:

Since the perimeters of the figures are equal, .

     (Subtract  from each side)

                            (Apply additive inverse property : )

                       (Subtract  from each side)

                                  (Apply additive inverse property : )

                             (Divide each side by )

                           (Simplify)

Therefore, the width of the rectangle is .

a.

Rectangle:                                                                             Isosceles triangle:

b.

The expression for perimeter of the rectangle is (or) .

The expression for  perimeter of the isosceles triangle is (or) .

c.

The width of the rectangle is .