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3 years ago

the hypotenuse of a right triangle is 6 1 /2cm and its area is 7 1/2sq.cm. Calculate the length of its perpendicular sides.

Mathematics

1 answer:

Romashka-Z-Leto [24]3 years ago

8 0

Answer:

The Length of the triangle = 2.307 cm

Step-by-step explanation:

Step(i):-

Given hypotenuse of a right triangle is = 6 1 /2 cm

Let assume the height of the triangle h = $\frac{13}{2} c m$

Given Area of the triangle = 7 1/2 sq.cm.

A = $\frac{15}{2} sq .c m$

Step(ii):-

We know that Formula

Area of the triangle

$A = \frac{1}{2} base X height$

$\frac{15}{2} = \frac{1}{2}X b X \frac{13}{2}$

On calculation , we get

Base of the triangle (b) = $\frac{30}{13} = 2.307 c.m$

Conclusion:-

The length of the triangle = 2.307 c.m

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Two pipes can fill a tank in 19 minutes if both are turned on. If only one is used, it would take 49 minutes longer for the smal

a_sh-v [17]

Answer:

The time taken by smaller pipe to fill the tank alone is 74.2 min

Step-by-step explanation:

Given as :

The time taken by two pipes to fill tank = 19 min

Let the time taken by larger pipe to fill tank = y

And the time taken by smaller pipe to fill tank = x

According to question

The smaller pipe takes 49 minutes longer than larger pipe

I.e x = y + 49

Now,

$\dfrac{1}{x}$ + $\dfrac{1}{y}$ = $\dfrac{1}{49}$

Or, $\dfrac{1}{y + 49}$ + $\dfrac{1}{y}$ = $\dfrac{1}{49}$

Or, $\dfrac{y + 49 + y}{y^{2} + 49 y }$ = $\dfrac{1}{49}$

Or, 2 y + 49 = $\dfrac{y^{2}+49y }{19}$

Or, 19 × ( 2 y + 49 ) = y² + 49 y

Or, 38 y + 931 = y² + 49 y

Or, y² + 49 y - 38 y - 931 = 0

or, y² + 11 y - 931 = 0

Or, Applying quadratic equation method to calculate the value of y

so, y = $\frac{- b \pm \sqrt{b^{2}-4\times a\times c}}{2\times a}$

Or, y = $\frac{- 11 \pm \sqrt{11^{2}-4\times 1\times (-931)}}{2\times 1}$

Or, y = $\frac{- 1 \pm \sqrt{121+3724}}{2}$

or, y = $\frac{- 1 \pm \sqrt{3845}}{2}$

or, y = $\frac{- 1 \pm 62.008}{2}$

∴ y = 25.2 , - 36.5

So, The time taken by larger pipe = y = 25.2 min

and the time taken by smaller pipe to fill the tank = y + 49 = 25.2 + 49 = 74.2 min

Hence The time taken by smaller pipe to fill the tank alone is 74.2 min answer

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the hypotenuse of a right triangle is 6 1 /2cm and its area is 7 1/2sq.cm. Calculate the length of its perpendicular sides.​

the hypotenuse of a right triangle is 6 1 /2cm and its area is 7 1/2sq.cm. Calculate the length of its perpendicular sides.