# A rectangle 2

A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.

Result

a =  63.454 cm
b =  38.072 cm

#### Solution:

$d = 74 \ cm \ \\ a:b = 5:3 \ \\ \ \\ d^2 = a^2 + b^2 \ \\ b = \dfrac{ 3 }{ 5 } a \ \\ d^2 = a^2 + (\dfrac{ 3 }{ 5 } a)^2 \ \\ \ \\ a^2 = d^2 / (1 + \dfrac{ 3^2 }{ 5^2 } ) \ \\ \ \\ a = \dfrac{ d }{ \sqrt{ 1 + \dfrac{ 3^2 }{ 5^2 } } } = \dfrac{ 74 }{ \sqrt{ 1 + \dfrac{ 3^2 }{ 5^2 } } } \doteq 63.4545 = 63.454 \ \text { cm }$
$b = \dfrac{ 3 }{ 5 } \cdot \ a = \dfrac{ 3 }{ 5 } \cdot \ 63.4545 = 38.0724= 38.072 \ \text { cm } \ \\ \ \\ k = a/b = 63.4545/38.0724 = \dfrac{ 5 }{ 3 } \doteq 1.6667 \ \\ \ \\ d_{ 2 } = \sqrt{ a^2+b^2 } = \sqrt{ 63.4545^2+38.0724^2 } \doteq 73.9994 \ cm$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! #### Following knowledge from mathematics are needed to solve this word math problem:

Looking for help with calculating roots of a quadratic equation? Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. Tv screen The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen?
2. Diagonal of the rectangle Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.
3. Isosceles triangle The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
4. Algebra X+y=5, find xy (find the product of x and y if x+y = 5) Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
6. Expression with powers If x-1/x=5, find the value of x4+1/x4
7. Power Number ?. Find the value of x.
8. Theorem prove We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
9. Discriminant Determine the discriminant of the equation: ?
10. Calculation How much is sum of square root of six and the square root of 225?
11. Roots Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
12. Equation Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2. Solve quadratic equation: 2x2-58x+396=0 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry? The product of two consecutive odd numbers is 8463. What are this numbers? Calculate unknown number whose 12th power when divided by the 9th power get a number 27 times greater than the unknown number. Determine the unknown number. Solve the quadratic equation: m2=4m+20 using completing the square method