Question

The diagram shows a rectangle , ABCD . If the area of ABCD is 30cm


`30 {}^(2)`
, calculate the values of x and y​

Answer 1

First, let's find the clues that the question provides.

From the diagram, we know that the length of sides AB & CD are equal, that is, AB=CD since this is the property of a rectangle where they are parallel sides of the same length. Therefore:


`2 + x = 6 \\ x = 6 - 2 \\ x = 4`

Next, the question also tells you the area of the rectangle. The area of a rectangle is given by the formula, Area = Length x Heights. So, we can say that multiplying the side AB, which is the length, with side AD gives you the area:


`(y + 2)(6) = 30 \\ y + 2 = (30)/(6) \\ y = (30)/(6) - 2 \\ y = 3`

Hope this helps!