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Triss [41]
1 year ago
6

the longer leg of a right triangle is 4 cm longer than the shorter leg. the hypotenuse is 8cm longer than the shorter leg. Find

the side length of the triangle.length of the shorter leg__cm length of the longer leg__cmlength of the hypotenuse ___cm
Mathematics
1 answer:
m_a_m_a [10]1 year ago
6 0

Mark, this is the solution:

Let x to represent the length of the shorter leg of the right triangle. Thus,

x + 4 = Longer leg

x + 8 = Hypotenuse

Now, we use the Pythagorean theorem to solve for x, this way:

(x + 8)² = (x + 4)² + x²

x² + 16x + 64 = x² + 8x + 16 + x²

Like terms:

-x² +8x + 48 = 0

Multiplying by -1 at both sides:

x² - 8x - 48 = 0

(x -12) (x + 4) = 0

x1 = 12

x2 = -4

We take x1 because the length of a side can't be a negative value. In consequence, we have:

• Shorter leg = 12 cm

,

• Longer leg = 16 cm

,

• Hypotenuse = 20 cm

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3 years ago
the length of a rectangle is 3cm more than the width. find the length and the width if the perimeter of the rectangle is 98cm.
laila [671]

The perimeter of a rectangle is <u>length + length + width + width</u>.

We know that the length of a rectangle is 3cm more than its width, which gives us the equation:  (l for length and w for width)

l = 3 + w

We also know that the perimeter of the rectangle is 98cm, which gives us the equation:

98 = 2l + 2w         (equation for perimeter of a rectangle as noted above)

We can divide both sides of this equation by 2 to get:

49 = l + w

Now we'll stick l = 3 + w into the above equation, which gives us:

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Substituting w = 23 into the equation l = 3 + w gives us:

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7 0
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