Respuesta :
Answer:
48 cm²
Step-by-step explanation:
First it would be helpful to look at the Area formula... Area=length x width (Or, A= L*W). Although we don't know the width (W), we know that length (L) is 2 more cm longer. As such, L=W+2. In the formula we have... Area= W*(W+2). Apply the distributive property (i.e. distribute 'W' to both terms in the parentheses, and it simplifies to A= W² + 2w. Now we look at the perimeter formula. P= 2L + 2W. Again we replace L with (w+2). So... P= 2(2+w) + 2W. We distribute to simplify and perimeter equals... 2w+4+2W. We combine like terms to produce... P= 4W+4. Since we know that Perimeter = 28 cm, we set this equation equal to 28. ----> 28=4w+4. Solve equation for W (i.e. subtract 4 from both sides, divide by 4) and W=6. So now we have the width: 6 cm. Remember, L (length) is just 2 more than W. So, (6+2)= 8. L=8. Plug these numbers back into the Perimeter just to verify: 2(8) + 2(6) = 28. Checks out. Now since we know both length and width, plug in the values into the Area formula (Area =L x W) ---> 6 x 8= 48. Just check we can use our modified area equation (A= W² + 2W) -----> (6)^2 + (2 x 6) = 48. Checks out. So the final answer to the Area is 48 cm².
