Question

2,5
3.6,x

The two quadrilaterals are similar. What is the value of

Answer 1

A rectangle has a length of 3.4 ft. and a width of 5.7 ft. A larger similar rectangle has a length of 17 ft. What is the width of the larger rectangle?

Answer 2

A right isosceles triangle has side lengths of 13.2, 13.2, and 18.6 meters. What is the hypotenuse of a similar triangle with legs 4.4 meters in length?

Answer 3

A quadrilateral’s smallest side measures 29 mm and its largest side measures 38 mm. A similar quadrilateral’s largest side measures 95 mm. What is the measure of its smallest side?

Answer 4

x?
Since the quadrilaterals are similar, the corresponding sides are proportional. We can set up a proportion:

2/3.6 = 5/x

Cross-multiplying, we get:

2x = 3.6 * 5

2x = 18

Dividing both sides by 2:

x = 18/2

x = 9

So the value of x is 9.

Answer 5

Since the two rectangles are similar, the corresponding sides are proportional. We can set up a proportion:

3.4/5.7 = 17/x

Cross-multiplying, we get:

3.4x = 5.7 * 17

3.4x = 96.9

Dividing both sides by 3.4:

x = 96.9/3.4

x ≈ 28.5

So the width of the larger rectangle is approximately 28.5 ft.

Answer 6

Since the two triangles are similar, the corresponding sides are proportional. In the given right isosceles triangle, the legs have a length of 13.2 meters. In the similar triangle, the legs have a length of 4.4 meters.

Let x represent the length of the hypotenuse in the similar triangle. We can set up a proportion using the lengths of the corresponding sides:

13.2/18.6 = 4.4/x

Cross-multiplying, we get:

13.2x = 18.6 * 4.4

13.2x = 81.84

Dividing both sides by 13.2, we get:

x = 81.84/13.2

x ≈ 6.2

So the hypotenuse of the similar triangle with legs 4.4 meters in length is approximately 6.2 meters.

Answer 7

Since the two quadrilaterals are similar, the corresponding sides are proportional. In the first quadrilateral, the smallest side measures 29 mm. In the similar quadrilateral, the largest side measures 95 mm.

Let x represent the measure of the smallest side in the similar quadrilateral. We can set up a proportion using the lengths of the corresponding sides:

29/x = 95/38

Cross-multiplying, we get:

38 * 29 = 95 * x

1102 = 95x

Dividing both sides by 95, we get:

x ≈ 11.57

So, the measure of the smallest side in the similar quadrilateral is approximately 11.57 mm.