Express 27p as a percentage of £9
2 answers:
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Answer:
The diagram displaying triangle ABC and the relevant statement along with the answer options is attached.
According to this, the answer is: The length of DC is 28.
Explanation:
From the diagram and the data that segment AB equals segment AC, you comprehend that angles B and C of the isosceles triangle ABC are congruent.
Triangles BED and CFD possess two sets of congruent angles (angle B is congruent to angle D, and angles BED and DFC are congruent), indicating that triangles BED and CFD are similar.
This similarity leads to the proportional relationship:
- DE / DF = DB / DC
Given that the ratio of DE to DF is 5:7, we have:
- 5/7 = DB / DC
Also, it is stated that segment BC is 48.
From the figure:
- BC = DB + DC = 48.
This results in two equations:
- 5/7 = DB / DC
- DB + DC = 48.
Now, we define DC = x, which implies DB = 48 - x, leading to the equation:
- 5 / 7 = (48 - x) / x
Solve this:
- 5x = 7 (48 - x)... [multiplication property: multiply by x and 7]
- 5x = 336 - 7x... [distributive property]
- 12x = 336... [addition property: add 7x to both sides]
- x = 336 / 12... [division property: divide by 12]
- x = 28... [simplification]
Therefore, the length of segment x = DC = 28.
