Question

If BD = 16 yd and the area of rhombus ABCD is 72 yd^2, what is AC?

Answer 1

BD = 16 yd

Area of ABCD = 72 yd²

AC = ?

Area of rhombus, using diagonal:

`(1)/(2) * d1 * d2`

Therefore:

`(1)/(2) * 16 * ac = 72`

Then:

`(16ac)/(2) = 72`

Cross multiply the above into:

`16ac * 1 = 72 * 2 = 144 \\ 16ac = 144`

Divide by the coefficient of AC:

`(16ac)/(16) = (144)/(16)`

Final answer is 9 yd

Answer 2

`\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}`

Given:

▪
`\sf{Area\text{ ABCD=}(1)/(2)* AC* BD}`

▪
`\sf{Area = 72 yd^2}`

▪
`\sf{BD = 6yd}`

`\leadsto` Substitute the values:

`\longrightarrow \sf{72 = (1)/(2) * AC * 16}`

`\leadsto` Solve for AC:

`\longrightarrow \sf{72=8* AC}`

`\longrightarrow \sf{ (72)/(8)=(8* AC)/(8)}`

`\longrightarrow \sf{AC=9}`

`\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}`

`\large \bm{AC= \: 9 yd}`