Answer:
[tex]\sf x = \dfrac{3}{2} [/tex]
[tex]\sf DE = \dfrac{27}{2} [/tex]
Step-by-step explanation:
Given that [tex]\sf \triangle CDE \cong \triangle HIJ [/tex].
We know that corresponding sides of the congruent triangles are equal, we can set up the equation:
[tex]\sf DE = IJ [/tex]
Substitute the value and solve for x.
[tex]\sf 9x = 7x + 3 [/tex]
Now, solve for [tex]\sf x [/tex]:
[tex]\sf 9x - 7x = 3 [/tex]
[tex]\sf 2x = 3 [/tex]
[tex]\sf x = \dfrac{3}{2} [/tex]
Now that we have the value of [tex]\sf x [/tex], we can find [tex]\sf DE [/tex] by substituting it back into the expression for [tex]\sf DE [/tex]:
[tex]\sf DE = 9x [/tex]
[tex]\sf DE = 9 \times \dfrac{3}{2} [/tex]
[tex]\sf DE = \dfrac{27}{2} [/tex]
So, the value of [tex]\sf x [/tex] is [tex]\sf \dfrac{3}{2} [/tex] and the length of [tex]\sf DE [/tex] is [tex]\sf \dfrac{27}{2} [/tex].
