Teeth rented a truck for one day. There was a base fee of $18.95,and there was an additional charge $.99 for each mile driven. K
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Answer:
x = 7
Step-by-step explanation:
We can tell by looking at this triangle that this is a <u>45 45 90 triangle.</u>
In this situation, the hypotenuse is and the legs are both
.So if we look at the hypotenuse, we can tell that x, or the leg of the triangle, is 7.
45 45 90 triangles: This is a special triangle in which the angles of the triangle are 45 45 and 90 degrees. This means that the hypotenuse will be and the legs of the triangle will be
. You can usually use the Pythagorean theorem to solve the missing sides.
<em><u>Statement:</u></em>
The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.
<em><u>To find out:</u></em>
The length of the larger side of the right angled triangle.
<em><u>Solution:</u></em>
Let us consider x as the smaller side and y as the larger side.
Then, in the right angled triangle,
x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]
Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).
And if the larger side is increased by 3 cm, then the larger side will be (y + 3).
Then, in the new right angled triangle,
(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]
or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²
or, x² + 4x + 4 + y² + 6y + 9 = (√117)²
or, x² + y² + 4x + 6y + 13 = (√117)²
Now, put the value of x² + y² from equation (I),
or, (2√13)² + 4x + 6y + 13 = (√117)²
or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)
or, 52 + 4x + 6y + 13 = 117
or, 4x + 6y = 117 - 52 - 13
or, 4x + 6y = 52
or, 4x = 52 - 6y
or, x = ...(II)
Now, put the value of x of equation (II) in (I),
x² + y² = (2√13)²
or, + y² = 52
or, = 52
or, 52y²-624y + 2704 = 52 × 16
or, 52y² - 624y + 2704 - 832 = 0
or, 52y² - 624y + 1872 = 0
or, 52(y² - 12y + 36) = 0
or, y²-12y +36 = 0 ÷ 52
or, y²-12y +36 = 0
or, (y)² - 2 × 6 × y + (6)² = 0
or, (y - 6)² = 0
or, y - 6=0
or, y = 6
We have taken y as the length of the larger side of the right angled triangle.
So, the length of the larger side is 6 cm.
<em><u>Answer:</u></em>
6 cm
Hope you could understand.
If you have any query, feel free to ask.