Answer:
37 mm
Step-by-step explanation:
For the first smaller triangle,
Given,
Hypotenuse = 13mm
Base = 5mm
Therefore, According to Pythagoras Theorem
[tex] {hypotenuse}^{2} - {base}^{2} = {height}^{2} [/tex]
[tex] = > {13}^{2} - {5}^{2} = {h}^{2} [/tex]
[tex] = > 169 - 25 = {h}^{2} [/tex]
[tex] = > 144 = {h}^{2} [/tex]
[tex] = > h = \sqrt{144} [/tex]
=> h = 12 mm
Hence, we got the height of the smaller triangle.
Since,
Height of the smaller triangle = Base of the larger triangle = 12mm
So, for larger triangle,
Given,
Base = 12mm
Height = 35 mm
Hypotenuse = x mm
Therefore, According to Pythagoras Theorem
[tex]{hypotenuse}^{2}={base}^{2}+ {height}^{2} [/tex]
[tex] = > {x}^{2} = {12}^{2} + {35}^{2} [/tex]
[tex] = > {x}^{2} = 144 + 1225[/tex]
[tex] = > {x}^{2} = 1369[/tex]
[tex] = > x = \sqrt{1369} [/tex]
=> x = 37
Hence, the required value of x is 37 mm (Ans)
