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4. A right triangle has legs with lengths of 6 feet and 9 feet. The hypotenuse of the triangle, in feet,
is between:
A. 4 and 5
B. 6 and 9
C. 9 and 10
D. 10 and 11
E. 11 and 13

4 A Right Triangle Has Legs With Lengths Of 6 Feet And 9 Feet The Hypotenuse Of The Triangle In Feet Is Between A 4 And 5 B 6 And 9 C 9 And 10 D 10 And 11 E 11 class=

Sagot :

To solve for the hypotenuse or the longest side of the triangle, we can simply use the Pythagorean Theorum.

C^2 = A^2 + B^2
C^2 = (6)^2 + (9)^2
C^2 = 36 + 81
C^2 = 117
C = square root of 117
C = About 10.81 feet

So, in conclusion, the hypotenuse or the longest side of the triangle in feet is: D. Between 10 feet and 11 feet.
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Answer:

D. 10 and 11

Step-by-step explanation:

This problem would use pythagorean theorem because we're finding the hypotenuse of a right triangle. This is its standard equation:

[tex]a {}^{2} + {b}^{2} = {c}^{2} [/tex]

The legs represent [tex]a[/tex] and [tex]b[/tex] respectively, and [tex]c[/tex] represents the hypotenuse. After plugging in the legs' respective values, the equation looks like this:

[tex]6^{2} + {9}^{2} = {c}^{2} →36 + 81 = {c}^{2} →117 = c^{2} [/tex]

To isolate [tex]c[/tex], you would find the square root of [tex]117[/tex]. In this case, we're just finding which integers[tex] \sqrt{117} [/tex] is between. [tex]\sqrt{100}(=10)[/tex] is the closest integer value below [tex]\sqrt{117}[/tex] and [tex]\sqrt{121}(=11)[/tex] is the closest integer value above [tex]\sqrt{117}[/tex]. So the answer is D. 10 and 11.

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