Triangles

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GED Math › Triangles

Questions 1 - 10

What is the area of a right triangle if the hypotenuse is 10, and one of the side lengths is 6?

Explanation

To determine the other side length, we will need to use the Pythagorean Theorem.

Substitute the hypotenuse and the known side length as either or .

Subtract 36 from both sides and reduce.

Square root both sides and reduce.

The length and width of the triangle are now known.

Write the formula for the area of a triangle.

$A=\frac{1}{2}bh$

Substitute the dimensions.

$A=\frac{1}{2}(8)(6) = 24$

The answer is .

Determine the area of the triangle if the base is 12 and the height is 20.

Explanation

Write the formula for the area of a triangle.

$A=\frac{BH}{2}$

Substitute the base and height into the equation.

$A=\frac{(12)(20)}{2} = 6(20) =120$

The answer is:

What is the area of a right triangle if the hypotenuse is 10, and one of the side lengths is 6?

Explanation

To determine the other side length, we will need to use the Pythagorean Theorem.

Substitute the hypotenuse and the known side length as either or .

Subtract 36 from both sides and reduce.

Square root both sides and reduce.

The length and width of the triangle are now known.

Write the formula for the area of a triangle.

$A=\frac{1}{2}bh$

Substitute the dimensions.

$A=\frac{1}{2}(8)(6) = 24$

The answer is .

Determine the area of the triangle if the base is 12 and the height is 20.

Explanation

Write the formula for the area of a triangle.

$A=\frac{BH}{2}$

Substitute the base and height into the equation.

$A=\frac{(12)(20)}{2} = 6(20) =120$

The answer is:

Which of the following can be the measures of the three angles of an acute isosceles triangle?

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$

$32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$

$45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$

$50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$

$80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$

Explanation

For the triangle to be acute, all three angles must measure less than $90 ^{\circ }$ . We can eliminate $32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$ and $45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$ for this reason.

In an isosceles triangle, at least two angles are congruent, so we can eliminate $50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$ .

The degree measures of the three angles of a triangle must total 180, so, since $80 ^{\circ }+ 80 ^{\circ }+ 40 ^{\circ } = 200^{\circ }$ , we can eliminate $80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$ .

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$ is correct.

Which of the following can be the measures of the three angles of an acute isosceles triangle?

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$

$32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$

$45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$

$50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$

$80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$

Explanation

In an isosceles triangle, at least two angles are congruent, so we can eliminate $50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$ .

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$ is correct.

If the hypotenuse of a right triangle if 7, and a side length is 5, what must be the length of the missing side?

$2\sqrt{6}$

$\frac{7}{5}$

$\frac{5}{7}$

$\sqrt{74}$

$6\sqrt2$

Explanation

Write the formula for the Pythagorean Theorem.

Substitute the values into the equation.

Subtract 25 from both sides.

Square root both sides.

$a = \sqrt{24} = \sqrt{4}\cdot \sqrt{6} = 2\sqrt{6}$

The answer is: $2\sqrt{6}$

If the hypotenuse of a right triangle if 7, and a side length is 5, what must be the length of the missing side?

$2\sqrt{6}$

$\frac{7}{5}$

$\frac{5}{7}$

$\sqrt{74}$

$6\sqrt2$

Explanation

Write the formula for the Pythagorean Theorem.

Substitute the values into the equation.

Subtract 25 from both sides.

Square root both sides.

$a = \sqrt{24} = \sqrt{4}\cdot \sqrt{6} = 2\sqrt{6}$

The answer is: $2\sqrt{6}$

A right triangle has hypotenuse with length 20 and a leg of length 9. The length of the other leg is:

Between 17 and 18.

Between 18 and 19.

Between 16 and 17.

Between 15 and 16.

Explanation

By the Pythagorean Theorem, if we let be the length of the hypotenuse, or longest side, of a right triangle, and and be the lengths of the legs, the relation is