Answer:
Given:
Length ( l ) of a rectangle is 4 cm longer than its width ( w ).
Perimeter of the rectangle is 50 cm.
1. Express the relationships:( l = w + 4 ) (Length is 4 cm longer than width)Perimeter formula: ( 2(l + w) = 50 )
2. Substitute ( l = w + 4 ) into the perimeter equation: [ 2((w + 4) + w) = 50 ]
3. Simplify and solve for ( w ): [ 2(2w + 4) = 50 ] [ 4w + 8 = 50 ] [ 4w = 42 ] [ w = 10.5 ]
4. Find ( l ): [ l = w + 4 = 10.5 + 4 = 14.5 ]
5. Dimensions of the rectangle:Width ( w = 10.5 ) cmLength ( l = 14.5 ) cm
6. Calculate the area ( A ) : [ A = l \times w = 14.5 \times 10.5 = 152.25 ]
7. Conclusion:Dimensions of the rectangle are ( \boxed{10.5 \text{ cm} \times 14.5 \text{ cm}} ).Area of the rectangle is ( \boxed{152.25} ) square centimeters.
