Question

M Find the range of possible diagonal lengths in a parallelogram with the given side lengths. 4. 3 and 12 5. x and 2x 6. x and x 812a, 25) F C12a + 2c, 25) The area of a parallelogram is given by the formula A=bh, where A is the area, b is the length of a base, and h is the height perpendicular to the base. ABCD is a parallelogram. E, F, G, and Hare the midpoints of the sides. 7. Show that the area of EFGH is half the area of ABCD. G A(0,0) D(200)

Answer 1

`\begin{gathered} \text{The range of the length of the diagonal is;} \\ \\ x\text{ }\pm\text{ }\sqrt[]{2} \end{gathered}`

Here, we want to find the range of the diagonal length of a parallelogram measuring x by x units

From what we have, we can see that the sides are equal and what this mean is that we have a square with equal diagonal length from any of the sides

So to get the diagonal length, we use the Pythagoras' theorem since the dsigonal splits the square into two equal parts

Thus, we have;

`\begin{gathered} d^2=x^2+x^2 \\ \\ d^2=2x^2 \\ \\ d\text{ = x}\sqrt[]{2} \end{gathered}`

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