Question

The difference between sides at right angles in a right angled triangle is 14

cm. The area of the triangle is 120 cm2

. Find the length of any side of right angled

triangle.​

Answer 1

Answer:

• Side 1 = 10 units
• Side 2 = 24 units

Steps:

Let side 1 be 'x' and side 2 be 'y'

According to the question,

⇒ x - y = 14

⇒ y = x + 14   ...(i)

Now according to the question,

Area of a triangle = 0.5 × base × height = 120 cm²

⇒ 120 cm² = 0.5 × x × ( x + 14 )

⇒ 120 / 0.5 = x² + 14x

⇒ 240 = x² + 14x

⇒ x² + 14x - 240 = 0    ...(ii)

Solving (ii) we get:

⇒ x² + 24x - 10x - 240 = 0

⇒ x ( x + 24 ) - 10 ( x + 24 ) = 0

⇒ ( x - 10 ) ( x + 24 ) = 0

⇒ x = 10 ; x = -24

Side cannot be a negative value. Hence the value of Side 1 ( x ) is 10 units.

Hence the measure of side 2 is ( x + 14 ) = 24 units.

Answer 2

Step-by-step explanation:

Answer:

1 ) If a function intersects or cuts the y-axis at a point ( 0,y ), then the distance between the origin to that point is termed as y - intercept. (Distance between (0,0) to (0,y).) In simpler terms, the value of 'y' when the value of 'x' is 0.

In this question, the function cuts the y-axis at (0,140). Hence the y-intercept of this graph is 140. It shows that, 140 children tickets (y) are sold when adult tickets (x) sold is equal to zero.

2 ) If a function intersects at a point (x,0), then the distance between the origin to that point is termed as x - intercept. In simple, it is the value of 'x' when the value of 'y' is 0.

In this question, the function intersects at (70,0). Hence the x-intercept is 70. It shows that when Children tickets (y) sold is zero, then number of adult tickets (x) sold is 70.

3 ) From the graph we can see the corresponding values of children tickets for the number of adult tickets sold. According to it, if 40 adult tickets are sold, the number of children tickets sold is 60.

4 ) Similar to last question, if 100 children tickets are sold, the number of adult tickets sold is 20.

5 ) Slope of the line is given by the formula:

Slope=Value of vertical changeValue of horizontal change\boxed{Slope = \dfrac{\text{Value of vertical change}}{\text{Value of horizontal change}}}

Slope=

Value of horizontal change

Value of vertical change

⟹Slope=14070=2\implies \boxed{Slope = \dfrac{140}{70} = 2}⟹

Slope=

70

140

=2

But since the graph is having an obtuse angle on clockwise rotation (Rotation from x-axis towards y-axis), the slope is in negative. Therefore the Slope of the line is -2.

6 ) The Slope of the line refers to the change of y-axis w.r.t change in x-axis.

According to this problem, it is the change of number of Children tickets w.r.t to change in the number of Adult tickets.

These are the required answers.