In the diagram below, OL is perpendicular to DX.
Pro
No 13
Tea
Find the length of OX

Line OX = 7.09

Explanation:

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SOLUTION

Given:

Line OL is perpendicular to DX

Line DX = 13

Line PO = the hypotenuse of the larger triangle

Line PO = 10

Line BO = hypotenuse of smaller triangle

Line BO = 12

To find length of line OX, we would apply rule of similar and congruent triangles.

∆DPO = ∆XBO

<POD = <BOX

Line DP is parallel to line XB

Since length of side DX = 13

Side DX = side DO + side OX

Let side DO = x

Side OX = 13-x

(Adj of ∆DPO)/(Adj of ∆XBO) = hyp of ∆DPO/hyp of ∆XBO

DO/OX = PO/BO

x/ (13-x) = 10/12

12x = 10(13-x)

12x = 130-10x

12x +10x = 130

22x = 130

x = 130/22 = 65/11

x is approximately = 5.91

Therefore line OX = 13 - 5.91

Line OX = 7.09