Sides of right angled triangle

One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.

Correct answer:

a =  4 m
b =  3 m
c =  5 m

Step-by-step explanation:

$$\begin{gathered} a=c-1 \\ b=c-2 \\ {a}^2+b^2=c^2 \\ (c-1{)}^2+(c-2{)}^2=c^2 \\ {c}^2-6c+5=0 \\ p=1;q=-6;r=5 \\ D=q^2-4pr=6^2-4\cdot 1\cdot 5=16 \\ D>0 \\ {c}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{6\pm \sqrt{16}}{2}} \\ {c}_{1,2}={\displaystyle \frac{6\pm 4}{2}} \\ {c}_{1,2}=3\pm 2 \\ {c}_1=5 \\ {c}_2=1 \\ \text{ Factored form of the equation: } \\ (c-5)(c-1)=0 \\ c>2 \\ c=c_1=5 \\ a=c-1=5-1=4\text{ m} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=c-2=5-2=3\text{ m}$

$c=5=5\text{ m}$

Try another example

Related math problems and questions:

• Euclid theorems
  Calculate the sides of a right triangle if leg a = 6 cm, and a section of the hypotenuse, which is located adjacent to the second leg b is 5cm.
• One leg
  One leg of a right triangle is 1 feet longer than the other leg. The hypotenuse is 5 feet. Find the lengths of the three sides of the triangle.
• RT perimeter
  The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference.
• R triangle
  Calculate the right triangle area whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
• RT leg and perimeter
  Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.
• Right triangle eq2
  Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
• Right triangle
  Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
• Two similar
  Two similar triangles, one has a circumference of 100 cm, the second has sides successively 8 cm, 14 cm, 18 cm longer than the first. Find the lengths of its sides.
• Right angled triangle 2
  LMN is a right-angled triangle with vertices at L(1,3), M(3,5), and N(6,n). Given angle LMN is 90° find n
• RT sides
  Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
• Leg
  Determine the trapezoid area with bases 71 and 42, and the height is 4 shorter than its leg.
• Rectangular triangle
  The lengths of the rectangular triangle sides with a longer leg of 12 cm form an arithmetic sequence. What is the area of the triangle?
• Right angled triangle
  The hypotenuse of a right triangle is 17 cm long. When we decrease the length of legs by 3 cm, then decrease its hypotenuse by 4 cm. Find the size of its legs.
• Right triangle - ratio
  The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
• Right triangle eq2
  Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
• Diagonal 20
  Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
• Integer sides
  A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?