Answer:
The length of the hypotenuse is 2 square root of 13 ⇒ c
Step-by-step explanation:
The rule of the area of the right triangle is A = 
× leg1 × leg2, where
leg1 and leg2 are the sides of the right angle
∵ The area of a right triangle is 12 in²
∵ The ratio of the length of its legs is 2: 3
→ Let leg1 = 2x and leg2 = 3x
∵ leg1 = 2x and leg2 = 3x
→ Substitute them in the rule of the area above
∴ 12 = × 2x × 3x
∵ 2x × 3x = 6x²
∴ 12 = × 6x²
∴ 12 = 3x²
→ Divide both sides by 3 to find x²
∴ 4 = x²
→ Take √ for both sides
∴ x = 2
→ Substitute x in the expressions of leg1 and leg2 to find them
∴ leg1 = 2(2) = 4 inches
∴ leg2 = 3(2) = 6 inches
∵ hypotenuse = 
∴ hypotenuse = 
∵ The simplest form of 
= 2
∴ The length of the hypotenuse = 2 inches
Answer:
The statement is missing. The statement is -- "A ray can be part of a line."
The answer is : The converse is not true, so Jahmiah is correct.
Step-by-step explanation:
A conditional statement is represented by showing p → q. It means if p is correct or true, then q is also correct or true.
And the converse of p → q can be shown as q → p.
But we know that the converse of a statement is not always true, it may be true and may not be true.
In the context, the statement is " a ray can be a part of a line." And so the converse would be "A line can be a part of the ray".
So by definition we know that a line is continuous line having no end points, it extends in one direction. While a ray starts from a point and extends to infinity in one direction.
Thus ray is part of line but line is not a part of the ray. So the converse of the statement is not correct.
Hence, Jahmiah is correct.
Answer:
26 cm²
Step-by-step explanation:
The area of the rectangle whose dimensions are shown at the right and bottom is ...
(6 cm)(7 cm) = 42 cm²
The figure is smaller than that by the area of the space whose dimensions are shown at the right and in the middle left:
(4 cm)(4 cm) = 16 cm²
The figure area is then the difference ...
42 cm² - 16 cm² = 26 cm²
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<em>Alternate solution</em>
Draw a diagonal line between the lower right inside corner and the lower right outside corner. This divides the figure into two trapezoids.
The trapezoid at lower left has bases 7 and 4 cm, and height 6-4 = 2 cm. Its area is ...
A = (1/2)(b1 +b2)h = (1/2)(7 + 4)(2) = 11 . . . . cm²
The trapezoid at upper right has bases 6 cm and 4 cm and height 3 cm. Its area is ...
A = (1/2)(b1 +b2)h = (1/2)(6 + 4)(3) = 15 . . . . cm²
Then the area of the figure is the sum of the areas of these trapezoids, so is ...
11 cm² + 15 cm² = 26 cm²
_____
<em>Comment on other alternate solutions</em>
There are many other ways you can find the area of this figure. It can be divided into rectangles, triangles, or other figures of your choice. The appropriate area formulas should be used, and the resulting partial areas added or subtracted as required.
You can also let a geometry program find the area for you. (It is 26 cm².)
Answer:
Step-by-step explanation:
The area of a triangle is given by
where
b is the base
h is the height
Here we have an equilateral triangle, which has the 3 sides of the same length.
Let's call L the length of one side.
We know that the perimeter of the triangle is
p = 9 in
The perimeter is the sum of the three sides, so:
Therefore, we find the length of the side:
Therefore the length is the base of the triangle,
The height can be calculated by considering half triangle: the hypothenuse is equal to L, while one side is equal to half the base (b/2), therefore the height is given by Pythagorean's theorem:
Therefore, the area of the triangle is:
