A shape of rectangle from which a smaller rectangle part is removed. If the remaining area of the larger rectangle is 35 cm squared, find k.

Question

Bigger rectangle: l = 2k + 6

                                w = k

Smaller rectangle( the remove part from the bigger): l = k

                                                                                               w = 3

 

Please help me and thank you in advance.

 

 

Answer 1

Area of bigger rectangle = (2k+6)(k)=2k² + 6k

 

Area of smaller rectangle = k*3 = 3k

 

 

The remaining area = 2k² + 6k -3k
                    

                            = 2k² + 3k

 

Since the area is 35 cm²

2k² + 3k = 35
2k² + 3k - 35 = 0
(2k -7)(k + 5) = 0
k = 3.5 or k = -5

Since the length cannot be negative

 

k = 3.5.