Triangle DEF is similar to triangle PQR. Side DE measures 3, side EF measures 7 and side FD measures 9. Side PQ measures 5x – 25 and side QR measures 6x + 4. Find the value of x.
Since triangle DEF similar to triangle PQR. Therefore, their corresponding sides are in the ratio.
DE/EF=PQ/QR
3/7=5x-25/6x + 25
On solving the equation we x = 11
To find the value of x, we need to set up a proportion between the corresponding sides of the two similar triangles.
In similar triangles, the corresponding sides are in proportion. So, we can write the proportion as:
DE/PQ = EF/QR
Substituting the given values:
3 / (5x - 25) = 7 / (6x + 4)
To solve this proportion, we can cross-multiply:
3 * (6x + 4) = 7 * (5x - 25)
Simplifying the equation:
18x + 12 = 35x - 175
Bringing the variables (x terms) to one side and the constant terms to the other side:
18x - 35x = -175 - 12
-17x = -187
To isolate x, divide both sides of the equation by -17:
x = (-187) / (-17)
Simplifying the division:
x = 11
Therefore, the value of x is 11.