Question

Determine the value of x in the kite.

A) 1/2

B) -2/5

C) 8

D) 2

Answer 1

Diagonals of kite cuts each other at 90°

so

Two isosceles triangles are formed

Hence sides are equal

• 10x-12=8
• 10x=8+12
• 10x=20
• x=2

Answer 2

D) 2

Explanation:

A kite is a quadrilateral with two pairs of adjacent sides of equal length. Its diagonals intersect at a 90° angle, forming two pairs of congruent right triangles.

The given diagram shows a kite where the pair of longest congruent adjacent sides are labelled (10x - 12) and 8. To determine the value of x, set the expressions for these congruent sides equal to each other and solve for x.

`\begin{aligned}10x-12&=8\\\\10x-12+12&=8+12\\\\10x&=20\\\\(10x)/(10)&=(20)/(10)\\\\x&=2\end{aligned}`

Therefore, the value of x is 2.