the two quadrilaterals are similar. what is the value of x
smaller quadrilateral: 2 and 5
bigger quadrilateral: 3.6 and x
To determine the value of x, we can set up a proportion between the corresponding sides of the two similar quadrilaterals.
The ratio of corresponding sides in similar shapes is equal. Therefore:
2/3.6 = 5/x
Cross multiplying, we have:
2x = 3.6 * 5
2x = 18
Dividing both sides by 2:
x = 9
Therefore, the value of x is 9.
To find the width of the larger similar rectangle, we can set up a proportion between the lengths and widths of the two rectangles.
Let's set up the proportion:
Length of smaller rectangle / Length of larger rectangle = Width of smaller rectangle / Width of larger rectangle
3.4 ft / 17 ft = 5.7 ft / x
Cross multiplying, we have:
3.4x = 17 * 5.7
3.4x = 96.9
Dividing both sides by 3.4:
x = 96.9 / 3.4
x ≈ 28.5
Therefore, the width of the larger rectangle is approximately 28.5 ft.
To find the hypotenuse of the similar triangle, we can set up a proportion between the corresponding sides of the two triangles.
Let's set up the proportion:
Leg of the smaller triangle / Leg of the larger triangle = Hypotenuse of the smaller triangle / Hypotenuse of the larger triangle
4.4 m / x = 13.2 m / 18.6 m
Cross multiplying, we have:
4.4 * 18.6 = 13.2 * x
81.84 = 13.2 * x
Dividing both sides by 13.2:
x = 81.84 / 13.2
x ≈ 6.2
Therefore, the hypotenuse of the similar triangle with legs 4.4 meters in length is approximately 6.2 meters.