One leg of a right-angled triangle is 7 cm larger than the second. the sum of the two legs is 17 cm.

One leg of a right-angled triangle is 7 cm larger than the second. the sum of the two legs is 17 cm. Find the area of a triangle.

To solve this example, we introduce two conditional variables “X” and “Y”, with the help of which we express the lengths of the larger and smaller legs of a right-angled triangle, respectively.

Based on the information in the example, we compose a system of equations:

1) X – Y = 7;

2) X + Y = 17.

Solving the system of equations, we get X = 7 + Y.

By inserting X into the second equation, we get 7 + Y + Y = 17 or 2Y = 17 – 7 = 10 or Y = 10/2 = 5 cm.

Therefore, X = 7 + 5 = 12 cm.

This means that the area of a right-angled triangle is 12 x 5/2 = 6 x 5 = 30 cm ^ 2.

Answer: 30 cm ^ 2.