Answer:
117 units
Step-by-step explanation:
if you use the ratio of the two longest sides then you can find all side lengths
[tex]\frac{52}{20}[/tex] = [tex]\frac{x}{10}[/tex]; x = half of 52, or 26
[tex]\frac{52}{20}[/tex] = [tex]\frac{x}{15}[/tex]; 20x = 52 · 15
20x = 780
x = 39
add to get perimeter: 52 + 26 + 39 = 117 units
Perimeter of the larger triangle is 117 units
Given
Two triangles are similar. The smaller triangle has side lengths 10, 20, and 15 units.
When the triangles are similar then the sides are in proportion
the longest side of the smaller triangle is 20 units
The larger triangle's longest side is 52 units.
Lets find out the unknown sides of largest triangle
Let x and y be the unknown sides . Make a proportion and solve for x and y
[tex]\frac{52}{20}=\frac{x}{10} \\x=\frac{52}{20} \codt 10\\x=26\\\\\\\frac{52}{20}=\frac{y}{15}\\y=\frac{52}{20} \codt 15\\y=39[/tex]
The unknown sides of largest triangle is 26 and 39 units
To find out the perimeter add all the sides of largest triangle
Perimeter =[tex]26+39+52=117[/tex]
Perimeter of the larger triangle is 117 units
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