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A quadrilateral ABCD has sides [tex]|AB| = 8 \, \text{cm}, \, |BC| = |AD| = 6.5 \, \text{cm}[/tex], [tex]\angle ABC = 60^{\circ}[/tex], and [tex]\angle BAD = 75^{\circ}[/tex].

1. Construct the locus [tex]l_1[/tex] of points equidistant from A and B.
2. Construct the locus [tex]l_2[/tex] of points equidistant from B and C.
3. Locate point P, where P is the point of intersection of [tex]l_1[/tex] and [tex]l_2[/tex].

Measure the diagonals of quadrilateral ABCD.

A rectangle measures 7.4 cm by 10.3 cm. Measure the length of the diagonal of this rectangle.



Answer :

GinnyAnswer
To solve the problem and measure the length of the diagonal of a rectangle with the given dimensions, we need to follow the geometric properties of the rectangle. Here's the step-by-step solution:

1. Understanding the problem:
We have a rectangle with the dimensions of 7.4 cm in length and 10.3 cm in width. We need to measure the diagonal of this rectangle.

2. Recalling the properties of a rectangle:
A rectangle has right angles (90°) at each corner. The diagonal of a rectangle divides it into two right-angled triangles, and within each triangle, we can apply the Pythagorean theorem.

3. Using the Pythagorean theorem:
The Pythagorean theorem states:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
where [tex]\(c\)[/tex] is the hypotenuse (diagonal in this case), and [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are the other two sides (length and width of the rectangle).

4. Assigning values:
In our case:
[tex]\[ a = 7.4 \text{ cm} \][/tex]
[tex]\[ b = 10.3 \text{ cm} \][/tex]

5. Calculating the diagonal:
Substituting the values into the Pythagorean theorem:
[tex]\[ c = \sqrt{(7.4)^2 + (10.3)^2} \][/tex]

6. Finding the numerical result:
The calculated length of the diagonal is:
[tex]\[ c \approx 12.68266533501535 \text{ cm} \][/tex]

So, the length of the diagonal of the rectangle measuring 7.4 cm by 10.3 cm is approximately 12.68 cm.