The question is an illustration of similar triangles where [tex]\triangle HIJ \sim \triangle HKL[/tex].
The length of IJ is 156.58 meters.
Given that:
[tex]KI = 70m[/tex]
[tex]HK = 145m[/tex]
[tex]KL = 105.6m[/tex]
From the figure, we can see that:
[tex]\triangle HIJ \sim \triangle HKL[/tex] --- triangles HIJ and HKL are similar
This means that:
[tex]\frac{HK}{KL} = \frac{HI}{IJ}[/tex] --- equivalent ration
Where:
[tex]HI = HK + KI[/tex]
[tex]HI = 145m + 70m[/tex]
[tex]HI = 215m[/tex]
So, we have:
[tex]\frac{HK}{KL} = \frac{HI}{IJ}[/tex]
[tex]\frac{145m}{105.6m} = \frac{215m}{IJ}[/tex]
Cross multiply
[tex]IJ \times \frac{145m}{105.6m} = 215m[/tex]
Cross multiply
[tex]IJ = 215m \times \frac{105.6m}{145m}[/tex]
[tex]IJ = 215m \times \frac{105.6}{145}[/tex]
[tex]IJ = \frac{215m \times 105.6}{145}[/tex]
[tex]IJ = 156.5793m[/tex]
Approximate
[tex]IJ = 156.58m[/tex]
Hence, the length of IJ is approximately 156.58 meters.
Read more about similar triangles at:
https://brainly.com/question/19739157
