Question

Can i pls have help on b

thank you

Answer 1

Answer:
`\frac {5} {2}`

Explanation:

As this is a kite, AD = CD and AB = BC. Thus,
`(4x - 2) + (4x - 2) + 3 \cdot (4x-2) + 3 \cdot (4x-2) = 64.`

This simplifies down to
`32x - 16 = 64.` Solving for x,
`x= \frac {80} {32} = \frac {5} {2}`

Answer 2

x = 2.5

Explanation:

Pre-Solving

We are given kite ABCD. We know that the measure of AB is 4x-2 and from part B, AD = 3AB, meaning that AD = 3(4x-2) = 12x - 6. Furthermore, we know that the perimeter of the kite is 64 cm.

We want to find the value of x.

Recall that a kite has 2 pairs of congruent sides; AB is congruent to BC, and AD is congruent to DC.

Also recall that the perimeter is simply the sum of all the lengths of the sides.

Solving

Because AB is congruent to BC, it means that the value of BC is also 4x - 2. Also, since AD is congruent to DC, the value of DC is 12x - 6 as well.

This means that our perimeter is:

AB + BC + AD + DC = 64

This can be substituted to become:

4x - 2 + 4x - 2 + 12x - 6 + 12x - 6 = 64

Now, simplify:

32x - 16 = 64

Add 16 to both sides.

32x = 80

Divide both sides by 32.

x = 2.5