Question

Please help me on these! I really don't get it and I have to get them done!

Answer 1

Hey there :)

All these shapes are known as a rhombus.
The are formula of a rhombus is $\frac{(side1)(side2)}{2}$

1st ) The area is given = 48 in² 
       The diagonals are 1) 8 in and 8 in = 16 in , 2) x in and x in = 2x in

Apply the formula to find x 
$48=\frac{(16)(2x)}{2}$
48 = 16x

Divide by 16 on either side to isolate x
$\frac{48}{16}= \frac{16x}{16}$
3 = x 

Check:
Area = $\frac{(8+8)(3+3)}{2}$ 
         = $\frac{96}{2}$
         = 48 in²

2nd ) Area is given = 48 ft²
          The diagonals are 1) 4 + 4 = 8 ft , 2) x

Apply the formula to find x 
48 = $\frac{(8)(x)}{2}$
48 = 4x

Divide by 4 on either side
$\frac{48}{4} = \frac{4x}{4}$
12 = x 

Check:
Area = $\frac{(4+4)(12)}{2}$
         = $\frac{96}{2}$
         = 48 ft²

3rd ) Given diagonals are 19 ft and 38 ft
Area = $\frac{(19)(38)}{2}$
         = $\frac{722}{2}$
         = 361 ft²

Answer 2

1stis 3x
2cnd is 12x
3rd is 361 ft squared