Question

ABCD is a rhombus with each side being equal to 8 cm. If BD = 10 cm, AC = 2√x cm , what is the value of √x +10

Answer 1

The value of ✓x+10 will be -

In the diagram below, ABCD is rhombus.

AC and BD are two diagonals of the ABCD rhombus.

All the angles, AOB,BOC,COD,AOD are 90°. (Rhombus's property)

Now,

For the right angle triangle BOA,

OB²+OA² = AB²

And, (OB = 1/2× BD = 10/2 = 5 cm)

Mathematical form will be,

(5)²+ (OA)² = (8)²

25+OA = 64

OA = 64-25

OA = 39 cm

Now, AC = 2× OA = 39×2 = 78 cm

As mentioned in the question,

78 = 2√x

✓x = 78/2

✓x = 36

So, the value of ✓x+10 is = 36+10 =46 (answer)