The table shows the relation between the side lengths of squares and their perimeters. Find the values of 𝑎, 𝑏 and 𝑐.
There are two rows in our table. The first row shows the side length in centimeters. And we know from the first sentence that this is talking about the side length of a square. So our three different squares have side length of five centimeters, 10 centimeters, and an unknown amount in the last box. This is one of the values we need to find 𝑐. The second row of our table shows us the perimeter in centimeters for each square. The first and second boxes we don’t know. We need to find the values of 𝑎 and 𝑏. And although we don’t know the side length of the third square, we are told the perimeter, which is four centimeters.
So our task is to find the values of the three missing numbers 𝑎, 𝑏, and 𝑐. Before we start, let’s remind ourselves about squares. What do we know about these shapes? We know that squares have four sides. And importantly, we know that those sides are all equal in length. So if we know one side, we can find the perimeter. We can see that the first square in the table has a side length of five centimeters. And because of the two facts we’ve just discussed, squares have four sides and they’re all equal, we can work out the perimeter. So to find the perimeter, we need to multiply five centimeters by four. Four fives are 20. So we know the perimeter of the first square is 20 centimeters. So we can complete the value of 𝑎 with 20; 𝑎 equals 20.
Now, let’s think about the second square mentioned in our table. We can see that the side length of our square in centimeters is 10 centimetres. So once again, we can use what we know about squares to help us find the perimeter. Squares have four equal sides. So to find the perimeter of the shape, all we have to do is to multiply 10 centimeters by four. We know four times 10 equals 40. So we can complete the missing number in this column with the value 40. We know 𝑏 is equal to 40. If we look at the final square in our table, we don’t know the side length. This is a missing number that we need to find. But we do know its perimeter. The perimeter of the square is four centimeters. We can see that in the bottom box. We need to find the value of each side.
Squares, as we know, have four equal sides. as We keep saying so if we divide four centimeters divided by four, we can find the length of one side. Four divided by four equals one centimetre. And this is the length of one of our sides. This will give us a square with a perimeter of four centimeters. We can complete the missing number in our final column with the number one. We found the values of 𝑎, 𝑏 and 𝑐 by applying our knowledge of the properties of squares. We know that squares have four sides and they’re all equal. And so we use the side length we were given to help find the perimeters. And then we work backwards by using the perimeter we were given to find the side lengths. The values of each letter are 𝑎 equals 20, 𝑏 equals 40, and 𝑐 equals one.