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Fantom [35]
3 years ago
10

Suppose the lengths of two sides of a right triangle are represented by 2x and 3 (x + 1), and the longest side is 17 units. Find

the value of x.
Mathematics
2 answers:
densk [106]3 years ago
6 0

Answer:

x=4

Step-by-step explanation:

<u>Step 1</u>:-

given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.

AB = 2x and BC = 3(x+1) and longest side AC= 17

by using Pythagoras theorem

AC^2 = AB^2 + BC^2

<u>step 2:-</u>

The hypotenuse is longest side is AC = 17 units

(17)^2 = 4x^2 +9(X+1)^2

on simplification, we will use formula

(a + b)^2 = a^2 +2ab+b^2

289 = 4x^2 +9(x^2+2x+1)

13x^2 +18x-280 = 0

finding factors  70 X 52 = 3640

13x^2 +70x-52x-280 = 0

13x^2 -52x+ 70x-280 = 0

Taking common , we get

13x(x-4)+70(x-4)=0

x-4=0 and 13x+70=0

x=4 and 13x =-70

x=4 and x=\frac{-70}{13}

we can not choose negative value so x value is 4

Final answer:- x = 4

<u>verification:-</u>

<u></u>AC^2 = AB^2 + BC^2<u></u>

289 = 4(4)^2+9(4+1)^2

289 = 64 +9(25)

289=289

Ghella [55]3 years ago
4 0

Answer:

x = 4

Step-by-step explanation:

The length of two legs of a right angle triangle are 2x and 3(x+1).  

The length of longest side is 17 units. It means measure of hypotenuse is 17 units.

According to the pythagoras theorem,

leg_1^2+leg_2^2=hypotenuse^2

(2x)^2+(3(x+1))^2=(17)^2

4x^2+9(x^2+2x+1)=289

4x^2+9x^2+18x+9=289

13x^2+18x-280=0

On splitting the middle terms we get

13x^2+70x-52x-280=0

x(13x+70)-4(13x+70)=0

(13x+70)(x-4)=0

Using zero product property we get

13x+70=0\Rightarrow x=-\dfrac{70}{13}

x-4=0\Rightarrow x=4

The value of x can not be a negaive number, because for negative value of x the value of 2x is negative and side can not be negative.

Therefore, the value of x is 4.

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