Question

One diagonal of a kite is twice as long as the other diagonal. If the area of the kite is 400 square meters, what are the lengths of the diagonals?

Answer 1

The lengths of the diagonals of a kite, where the area is 400 square meters and one diagonal is twice the length of the other, are 20 meters for the shorter diagonal and 40 meters for the longer diagonal.

Step-by-step explanation:

You asked how the lengths of the diagonals of a kite can be determined given that the area is 400 square meters and one diagonal is twice as long as the other. To find the diagonals, we'll use the formula for the area of a kite, which is Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.

Let's denote the shorter diagonal as d, which means the longer diagonal is 2d. Plugging these into the area formula gives us:

400 m2 = (d * 2d) / 2

Multiplying both sides by 2 gives us 800 m2 = d * 2d, which simplifies to 800 m2 = 2d2.

Dividing both sides by 2 gives us 400 m2 = d2. Taking the square root of both sides, we find that d = 20 meters. Hence, the longer diagonal is 2 * 20 meters = 40 meters.

The lengths of the diagonals of the kite are 20 meters and 40 meters.

Answer 2

20m and 40m

Step-by-step explanation:

The area (A) of a kite is calculated using the formula

A =
`(1)/(2)` product of diagonals

Let one diagonal be d then the other diagonal is 2d ( twice as long )

Hence

`(1)/(2)` × 2d × d = 400

d² = 400 ← take the square root of both sides

d =
`√(400)` = 20

and 2d = 2 × 20 = 40

The diagonals are 20m and 40m in length