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

Answer:

Hey mate.. Here is your answer

Explanation:

Let the longer side be x

Then hypotenuse = 2+x

And shorter side=x-7

According to Pythagorus theorom

H^2=b^2+p^2

(2+x)^2=x^2+(x-7)^2

X^2+4+4x=x^2+x^2+49-14x

X^2+4x+4=2x^2-14x+49

0=x^2-18x+45

0=x^2-15x-3x+45

0=x(x-15)-3(x-15)

0=(x-3)(x-15)

X=3 or x=15

But x cannot be 3 as if it is 3 then shorter side will be -4

So x=15

Shorter side=8

Hypotenuse=17

Answer 2

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★ Gɪᴠᴇɴ :-

• Hypotenuse is 2cm greater than the longer side.
• Smaller side is 7cm smaller than the longer side

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★ Tᴏ Fɪɴᴅ :-

• Hypotenuse of the triangle.

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★ Sᴏʟᴜᴛɪᴏɴ :-

Let the longer side of the ∆ be x

Then , by the given information

• Smaller side = x - 7

• Hypotenuse = x + 2

• longer side = x

Now , finding x using Pythagoras theorem.

Pythagoras theorem :- Square of Hypotenuse equal to sum of squares of other two sides

→ (x + 2)² = (x - 7)² + x²

→ x² + 2(2)(x) + 2² = x² - 2(7)(x) + 7² + x²

→ x² + 4x + 4 = 2x² - 14x + 49

→ 2x² - 14x + 49 - (x² + 4x + 4) = 0

→ 2x² - 14x + 49 - x² - 4x - 4 = 0

→ x² - 18x + 45 = 0

Now , we got a quadratic equation , finding its roots by quadratic formula .

→ - (-18) ±√(-18)² - 4(1)(45)/2(1)

→ 18±√324 - 180/2

→ 20±√144/2

→ 20 ± 12/2

→ 2(10 + 6)/2 or 2(10 - 6)/2

→ x = 6 or 4

Now , finding hypotenuse

Hypotenuse = x + 3

Hypotenuse = 6 + 3 or 4 + 3

Hypotenuse = 9 or 7

Hence , hypotenuse = 9cm or 7cm

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