Question

8. In the given figure, find x, if ABCD is a rhombus and AE = 4 cm, ar(ABCD) = 20 cm²?
A. 4 cm
B. 5 cm
C. 10 cm
D. 2.5 cm​

Answer 1

Given:

Ar(ABCD)=20cm²

AE=4cm

To find:

The length of x

Solution:

The length of x is 2.5 cm. (Option D)

We can determine the length by following the given steps-

We know that the diagonals of the rhombus ABCD bisect each other and divide the rhombus into four triangles of equal area.

So, AE=EC=4 and DE=BE=x.

We are given that the area of the rhombus=20cm²

The area of the rhombus=4×area of ΔAED

The diagonals AC and BD intersect at 90°, so ΔAED is a right-angled triangle.

The area of ΔAED=1/2×AE×DE

So, the area of the rhombus=4×1/2×AE×DE

On putting the values,

20=4×1/2×AE×DE

5=1/2×AE×DE

5×2=4×x

10/4=x

2.5=x

Therefore, the length of x is 2.5 cm.

Answer 2

Answer:

The correct answer is D 2.5cm