Question

The hypotenuse of a right triangle is 2 cm more than the longer side of the triangle. The shorter
side of the triangle is 7 cm less than the longer side. Find the length of the hypotenuse.
Please help me my half Yearly is tomorrow I need answer fastest and reliable answer will be marked as brainliest​

Answer 1

Solution :

Let the longer side of the right angled triangle be x

Then, hypotenuse = (x + 2) and shorter side = (x - 7)

Here,

• h = x + 2

• p = x

• b = x - 7

Using Pythagoras Theorem :

★ (Hypotenuse)² = (Perpendicular)² + (Base)²

→ (x + 2)² = (x)² + (x - 7)²

→ x² + 2(x)(2) + 2² = x² + x² + 2(x)(7) - (7)²

→ x² + 4x + 4 = x² + x² + 14x - 49

→ x² - 18x + 45 = 0

→ x² - 15x - 3x + 45 = 0

→ x(x - 15) - 3(x - 15) = 0

→ (x - 3) (x - 15)

The value of x can't be 3 as (x - 7) would be negative.

Hence, the value of the longer side is 15 cm.

$\sf \: \therefore Hypotenuse = (15 + 2) = 17 cm$

Answer 2

Answer:

17 cm is the correct answer

Step-by-step explanation:

hope it helps you

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