Question

In square ABCE and right-angled triangle CDE, where DE = 4cm and CDE is 14cm², what is the length of AC?

A) 8cm
B) 10cm
C) 12cm
D) 14cm

Answer 1

The length of AC is equal to twice the length of one side of the square.

Step-by-step explanation:

To find the length of AC, we need to determine the length of the side of the square. Since ABCE is a square, all sides have the same length. Let's call this length x.

In right-angled triangle CDE, the area is given as 14 cm² and DE is given as 4 cm. The area of a triangle is found using the formula: Area = (1/2) * Base * Height. In this case, the base is DE and the height is CD. So, we can set up the equation:

14 = (1/2) * 4 * CD
28 = 4 * CD
CD = 7 cm

Since CD is the same as the side length of the square, we know that x = 7 cm.

Therefore, the length of AC is equal to the sum of AB and BC, which is equal to 2x:
AC = 2 * 7 cm = 14 cm.

So, the correct answer is D) 14cm.