Question

1)Find the scale factor of Figure A to Figure B.
2) Solve for the missing length of x.

Answer 1

x = 12

Explanation:

Here, we want to get the value of x

Looking at the angles of the shapes, we can see that the two figures are similar

When two figures are similar, the ratio of their corresponding sides are equal

Thus, mathematically, we have it that;

MN/PN = HJ/KJ

9/x = 6/8

9 * 8 = 6 * x

6x = 72

x = 72/6

x = 12

Answer 2

1) The scale factor of Figure A to Figure B is 5/9

2) x = 12

3) y = 10

Explanation:

1) The scale factor of figure 'A' to Figure 'B', is given by the ratio of the side of figure 'A' to the corresponding side of Figure 'B'

The corresponding longest sides of Figures 'A' and 'B' are, 36 and 20 respectively

The corresponding shortest sides of Figures 'A' and 'B' are, 25.2 and 14 respectively

Therefore, the scale factor of Figure A to Figure B = 20/36 = 14/25.2 = 5/9

Therefore, in order to get the dimension of Figure 'B' we multiply the dimension of Figure 'A' by 5/9

The scale factor of Figure A to Figure B = 5/9

2) Given that the quadrilaterals LMNP, and GHJK are similar

The scale factor of Figure LMNP to Figure GHJK = 4/6 = 2/3

Therefore, given that the corresponding side to segment NP of length 'x' in figure GHJK is segment JK

Therefore, the scale factor of NP to JK = 2/3

Length of JK = 2/3× Length of NP

Length of JK = 8

Length of NP = x

∴ 8 = 2/3 × x

x = 3 × 8/2 = 12

x = 12

3) Similarly, from the scale factor of Figure LMNP to Figure = 2/3, we have;

Length of GK = 2/3× Length of LP

Length of GK = y

Length of LP = 15

∴ y = (2/3) × 15 = 10

y = 10