# Rectangular triangle

The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?

Correct result:

S =  54 cm2

#### Solution:

$a=b-x \ \\ b=12 \ \text{cm} \ \\ c=b+x \ \\ \ \\ c^2=a^2 + b^2 \ \\ (12+x)^2=(12-x)^2 + 12^2 \ \\ 48x=144 \ \\ x=144/48=3 \ \\ \ \\ a=b-x=12-3=9 \ \text{cm} \ \\ c=b+x=12+3=15 \ \text{cm} \ \\ \ \\ S=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 9 \cdot \ 12 }{ 2 }=54 \ \text{cm}^2$

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!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Fifth member
Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.
• Arithmetic progression
In some AP applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d = ?
• Third member
Determine the third member of the AP if a4=93, d=7.5.
• Difference AP 4
Calculate the difference of the AP if a1 = 0.5, a2 + a3 = -1.1
• Determine AP
Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71
• AP 6
Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
• Sequence
Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an
• Sequence
Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
• Sequence 3
Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
• AP - simple
Determine the first nine elements of sequence if a10 = -1 and d = 4
• Square root 2
If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
• Evaluation of expressions
If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3