Question

ABCD is a parallelogram. The diagonals AC and BD intersect at
point M. The length of Seg. AC, AB and AD are 24, 22 and 34 respectively
Find the length of Seg. BD.​

Answer 1

Let us look at the Answer:

Step-by-step explanation:

We know that the diagonal of parallelogram divides it into 2 congruent triangles.

The area of triangle ABD, AB=22 AD= 34 BD = 24

⇒ a= 22 b = 34, c = 24  ⇒ s = 22+34+24/2 = 40

Using Heron's formula, Δ = √s(s-a)(s-b) (s-c)

Δ = √40 (40-24) (40-34) (40-22) = √40×16×6×18 = √2×2×2×5×2×2×2×2×2×3×2×3×3 = 2×2×2×2×3×√15 = 48√15

the area of parallelogram = 2× 48√15 = 96√15

Also, the area of parallelogram = 1/2 × product of diagonals

                                                   = 1/2 AC × BD

∴ 96√15 = 1/2 ×24 × BD ⇒ BD = 96√15 /12 = 6√15

Answer 2

Step-by-step explanation:

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