# Find the legs of a right-angled triangle if their sum is 46.

August 30, 2021 | education

| In this task, we will find the lengths of the legs of a right-angled triangle;

Since we know the sum of the lengths of the legs and the length of the hypotenuse then;

a + b = 46. where a, in the leg of a right-angled triangle;

Let us express the leg a;

a = 46 – b;

Let’s write down the Pythagorean theorem;

a ^ 2 + b ^ 2 = 34 ^ 2;

Let’s substitute the value of leg a;

(46 – b) ^ 2 + b ^ 2 = 34 ^ 2;

2116 – 92 * b + 2 * b ^ 2 = 1156;

2 * b ^ 2 – 92 * b + 960 = 0;

Let’s take the two out of the brackets and divide both parts by 2;

в ^ 2 – 46 * в + 480 = 0;

After solving this equation, we get such roots;

b1 = 30;

B2 = 16;

Let’s substitute leg a into the formula and get;

b1 = 46 – 30 = 16;

B2 = 46 – 16 = 30;

Since the answers are symmetrical then;

a = 30; h = 16.

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