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Korvikt [17]
3 years ago
10

Find the value of x.

Mathematics
1 answer:
marta [7]3 years ago
8 0

Answer:

\boxed {\boxed {\sf x=5}}

Step-by-step explanation:

We are given a quadrilateral. It will be difficult to find x using this shape, but we can drop a perpendicular line and create a right triangle (refer to the attached image).

Match up the other sides. The height is equal to 4.

At the base, the longer portion is 7 because the line segment above the base is 7. Since the entire base is 10, the smaller portion must be 3 because 10-7=3.

Now we have 2 sides of a right triangle and one unknown. We can use the Pythagorean Theorem.

a^2+b^2=c^2

Where <em>a</em> and <em>b</em> are the legs and <em>c</em> is the hypotenuse.

In this triangle, 4 and 3 are the legs because they make the right angle. x is the hypotenuse because it is opposite the right angle.

  • a= 4, b=3, c=x

Substitute the values into the formula.

(4)^2+(3)^2=x^2

Solve the exponents.

  • (4)²= 4*4= 16

16+(3)^2=x^2

  • (3)²= 3*3= 9

16+9=x^2 \\

25=x^2

Take the square root of both sides of the equation to isolate the variable.

\sqrt{25} =\sqrt{x^2}

5=x

<u>x is equal to 5. </u>

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