Two American flags of different dimensions are properly folded into two similar isosceles right triangles. The ratio of the length of the legs of the smaller triangle to that of the larger triangle is 4 : 5. If the length of the hypotenuse of the larger triangle is 2 feet, what is the length of the smaller triangle to the nearest tenth of a foot?

a. 0.1 ft

b. 0.6 ft

c. 1.6 ft

d. 2.5 ft

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

andromache andromache · Answer 2 · 2022-03-03T12:17:58+01:00

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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