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Let the sides be x and y:-

x+y = 17.5 => y = 17.5-x

0.5*xy = 37.5 => xy = 75

x(17.5-x) = 75 => 17.5x-x2-75 = 0

Solving the above quadratic equation gives x postive values of 10 and 7.5

So the sides are 10 cm and 7.5 cm

Using Pythagoras' theorem the length of the hypotenuse works out as 12.5 cm

Q: What is the length of the hypotenuse of a right angle triangle whose sides add up to 17.5 with an area of 37.5 square cm showing work?

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The length of the hypotenuse works out as the square root of 41

Square root of 41

To find the length of the hypotenuse on a triangle, you have to use the Pythogoras Theoram. using the equation a square + b square = c square. you cannot find it without using the pythagoras theoram

An isosceles right triangle will always have its shorter sides of the same length, and the hypotenuse will always be this length times sin(45o) or times the square root of 0.5.

In a right triangle, square the lengths of the other two sides and add them together. The length of the hypotenuse will be the positive square root of that number.

Related questions

The square of the length of the base plus the square of the length of the height will equal the square of the length of the hypotenuse of your right triangle, per Pythagoras. Square the hypotenuse, subtract the square of the height, and then find the positive square root of that and you'll have the base of your right triangle.

The length of the hypotenuse works out as the square root of 41

Sure, place a triangle's hypotenuse (longest side) on the other triangle's hypotenuse, that will give either a square or a rectangle. Then place the square on one end of the rectangle. For this to work though, the length of the square's side HAS to equal the length of the triangles hypotenuses, and likewise each triangle's hypotenuse much equal the length of a side of the square. Hope this is clear.

A right triangle only has two legs, the third side is called the hypotenuse . The square of the length of the hypotenuse is equal to the sum of the squares of the two legs. The square root of the difference of the square of the hypotenuse and the square of one leg is equal to the length of the other leg.

The square of the hypotenuse is equal to the length of the hypotenuse times itself. This is also equal to the sum of the squares of the other two sides in a right triangle.

the square root of 5

Square root of 41

A hypotenuse is the longest side of a right angled triangle. The length of a hypotenuse can be found using the Pythagorean Theorem. This states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This means that to find the length of the hypotenuse, you need to know the lengths of the other two sides.

Use Pythagoras' theorem: 42+42 = 32 and the square root of this is the length of the hypotenuse

in an isosceles triangle, if the legs have length L, then the hypotenuse has length L square root of 2

32 +82 =9+64=73 So the hypotenuse is of length square root of 73

To find the length of the hypotenuse on a triangle, you have to use the Pythogoras Theoram. using the equation a square + b square = c square. you cannot find it without using the pythagoras theoram