Respuesta :
Answer:
Option c. is correct
Step-by-step explanation:
Given: The ratio of the length of the legs of the smaller triangle to that of the larger triangle is 4 : 5.
Length of the hypotenuse of the larger triangle is 2 feet.
To find: length of the hypotenuse of the smaller triangle
Solution:
Consider two similar isosceles right triangles ABC and PQR right angled at B and Q respectively such that the ratio of the length of the legs of the smaller triangle to that of the larger triangle is 4 : 5. Here assume that the triangle PQR is the larger one.
[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{4}{5}[/tex] and PR = 2 feet
As the triangles are similar and sides of similar triangles are proportional,
[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR} \\\frac{4}{5}=\frac{AC}{2}\\ AC=\frac{4}{5}(2)\\ =1.6\,\,feet[/tex]
Option c. is correct
The length of the smaller triangle to the nearest tenth of a foot is option c. 1.6 feet.
Calculation of the length:
Since, the ratio of the length of the legs of the smaller triangle to that of the larger triangle is 4 : 5. And the length of the hypotenuse of the larger triangle is 2 feet.
So,
[tex]4\div 5 = AC\div 2\\\\AC = 4\times 2 \div 5[/tex]
AC = 1.6
Therefore, The length of the smaller triangle to the nearest tenth of a foot is option c. 1.6 feet.
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