Answer: The perimeter of the largest triangle = 117 units.
Step-by-step explanation:
Sides of smaller triangle = 10,20 and 15 units
Longest side = 20 units
Longest side of larger triangle = 52 units
Sides of two similar triangles are proportional.
Let k be proportionality constant.
[tex]k=\dfrac{\text{Length in larger triangle}}{\text{Length in smaller triangle}}[/tex]
[tex]k=\dfrac{52}{20}\\\\\Rightarrow\ k=\dfrac{13}{5}[/tex]
Length of other two sides,
[tex]10\times\dfrac{13}{5}, 15\times\dfrac{13}{5}\ i.e.\ 26\text{ units}, 39\text{ units.}[/tex]
So sides of larger triangle = 52 units, 26 units , 39 units
Perimeter of largest triangle = 52 +26+39 = 117 units
Hence, the perimeter of the largest triangle = 117 units.
