Mathematics, 31.01.2021 04:40 briarkaltvedt

One leg of a right triangle is more than 3 more inches than the shorter leg. The hypotenuse is 15 inches. What are the lengths of the legs of the triangle and what is the area?

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Answer from: chad65

1. 9 inches, 12 inches and 15 inches

2. 54 square inches

Step-by-step explanation:

1. The first part of this question would lead to a quadratic equation. Let the shorter leg be represented by x.

shorter leg = x

other leg = x + 3

hypotenuse = 15 inches

Applying the Pythagoras theorem, we have;

$/15/^{2}$ = $/x/^{2}$ + $/x+3/^{2}$

225 = $x^{2}$ + $(x+3)^{2}$

225 = $x^{2}$ + $x^{2}$ + 6x + 9

= 2 $x^{2}$ + 6x + 9

2 $x^{2}$ + 6x + 9 - 225 = 0

2 $x^{2}$ + 6x - 216 = 0

divide through by 2 to have

$x^{2}$ + 3x - 108 = 0

From the quadratic formula;

x = (-b ± $\sqrt{b^{2}-4ac }$ ) ÷ 2a

but, a = 1, b = 3, c = -108

x = (-3 ± $\sqrt{(3)^{2}-4(1)(-108)}$ ) ÷ 2

= (-3 ± $\sqrt{441}$ ) ÷ 2

= (-3 ± 21) ÷ 2

Thus,

x = (-3 + 21) ÷ 2 OR x = (-3 - 21) ÷ 2

x = 9 OR x = -12

So that, x = 9 inches

The shorter leg is 9 inches, and the other leg is 12 inches.

2. The area of the triangle can be determined by applying Heron's formula:

A = $\sqrt{s(s-a)(s-b)(s-c)}$

where s is the average value of the sum of the three sides a, b, and c.

Let, a = 9, b = 12 and c = 15

s = $\frac{a +b+c}{2}$

= $\frac{(9+12+15}{2}$

= 18

A = $\sqrt{18(18-9)(18-12)(18-15)}$

= $\sqrt{18*9*6*3}$

= $\sqrt{2916}$

A = 54

Area of the triangle is 54 square inches.

Answer from: Quest

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

Me? ! with this question which relationship is a function?

Answer from: Quest

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints

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One leg of a right triangle is more than 3 more inches than the shorter leg. The hypotenuse is 15 in...