The value of the distance across the lake IJ to the nearest hundredth is 158.66m
Similar triangles are triangles with equal corresponding angles and equal side ratio. This means that the ratio of the corresponding sides are equal.
Triangle HIJ is similar to triangle HKL
therefore;
let IJ = x
110+155)/155 = x/92.8
= 265/155 = x/92.8
155x = 265 × 92.8
155x = 24592
x = 24592/155
x = 158.66m
Therefore, the value of the distance across the lake IJ to the nearest hundredth is 158.66m