The difference between the legs of a right-angled triangle is 3 cm, and their sum

| April 27, 2021 | education

The difference between the legs of a right-angled triangle is 3 cm, and their sum is several times greater. Find the area and perimeter of this triangle.

Take one leg A, the other B. According to the first condition A-B = 3 cm, the second A + B = 15 (3 * 5).
An equation with two unknowns is obtained. It is necessary in the first equation to transfer B to the right side of the equation, we get A = B + 3cm. Change in the second condition A to the resulting equation.
We get (B + 3cm) + B = 15cm. Expand the brackets and get B + 3cm + B = 15cm. B + B gives us 2B. The result is the equation 2B + 3cm = 15cm. Find 2B. 2B = 15cm-3cm. As a result, 2B = 12cm. Find B. B = 12 cm / 2. B = 6 cm. We found B.
To find A, we substitute B into the first condition.
We get A-6cm = 3 cm. Calculate A. A = 3cm + 6cm. A = 9cm.
Now we know the length of the two legs. We calculate the area: S = 1 / 2AB. S = 1/2 * 9cm * 6cm = 9cm2.
Calculate the perimeter: P = A + B + √ (A² + B²) = 9 + 6 + √ (9² + 6²) = 15 + √ (81 + 36) = 15 + √117≈15 + 10.83 = 25.83.



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