Problem number 8 states, a rectangle with perimeter 30 cm is divided into 4 parts by a vertical line and a horizontal line. One of the parts is a square of area 9 cm squared as shown in the picture. What is the perimeter of rectangle ABCD? The problem gives us this diagram and tells us that the outside perimeter is equal to 30 cm, we'll call that P. The question asks for the perimeter of the rectangle ABCD, we'll call that Q. So let's consider the one spot that we have information, the top left square. We know the area of a square is the length of its side squared, so we know that a squared is equal to 9, where a is the side length of the square. Taking the square root we get that the side length is equal to 3. Now let's name the remaining unknown side lengths, they'll be called B and C. Let's consider the outer perimeter again, that we know to be 30 cm, and we know that the perimeter is the sum of the side lengths, so we have 4 segments of 3 cm, 2 segments of B, and 2 segments of C. Now let's do the same for the perimeter for rectangle ABCD. The perimeter consists of 2 segments of B and 2 segments of C. With this information we can actually solve for Q. We can notice that in the equation for P we have 2B plus 2C, which is in the equation for Q, so let's just substitute that in. Now let's substitute P with 30 cm. So we get 30 is equal to 4 times 3 plus Q. 4 times 3 is 12, subtract 12 from both sides and we get Q, 18, the perimeter of ABCD. So the question asked us, what is the perimeter of rectangle ABCD? The answer is 18, letter C.

perimeter

rectangle

geometry

mathematics

calculation