Question

8 As shown in the diagram of rectangle ABCD below, diagonals AC and BD intersect at E. С

Answer 1

The length of Ac would be 24.

The correct answer is option D.

As we can see in the diagram given that ABCD is a rectangle which implies that the diagonals of the rectangle would be equal.

So ,

AC = BD

Now , we are given that AE = x + 2 and BD = 4x -16

AE is half of AC

So,

2AE = BD ( because diagonals are equal AC = BD and AE and CE are divided into equal parts )

2( x + 2) = 4x - 16

2x = 4 = 4x - 16

-2x = -20

x = 10

So , the value of x is 10

Now as we know that the diagonals of rectangle are equal so

AC = BD

Substituting the value of x we found earlier in given expression for BD to find the value of BD.

BD = 4(10) - 16

= 40-16

= 24

So , the value of BD = 24 = Ac.

Hence the value of Ac is equal to 24 making option D the correct option.

Answer 2

From the rectangle given, we see the diagonals of the rectangle bisect each other at E.

From the properties of a rectangle is that;

1) The diagonals are congruent. That is, they are equal. AC = BD

2) The diagonals bisect each other into two equal parts.

These are the two properties we will use in solving the question