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The length of a rectangle is 4cm longer than it's width. if the perimeter is 50cm, what are the dimensions of the rectangle? (a) calculate it's area.

Sagot :

chakmasanjay13

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.

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